Parcells also decided Marshall is worth two second-round draft picks -- and a contract extension that makes him one of the NFL's best-paid pass catchers.
The Dolphins acquired the high-maintenance Pro Bowl wideout from the Denver Broncos on Wednesday in exchange for a second-round pick (43rd overall) in next week's draft and another selection next year. Marshall then flew to Miami and signed a four-year extension worth $47.5 million, with $29 million coming in the first three years, a league source told NFL Network's Jason La Canfora.
Marshall earned $2.2 million last season in the final year of the contract that he signed as a fourth-round pick in 2006. He signed his $2.521 million tender with the Broncos on Tuesday to facilitate a trade, and NFL.com's Steve Wyche reports that Marshall will play under that deal in 2010 before the extension starts.
Marshall fills the Dolphins' most glaring need: a go-to guy who will loosen up defenses for their potentially potent ground game and young, strong-armed quarterback Chad Henne. However, the former Central Florida star returns to the Sunshine State with plenty of issues.
Marshall caught at least 100 passes in each of the past three years, and he made the Pro Bowl the past two seasons, but the Broncos were willing to part with him because he became a chronic headache. He has a history of domestic violence, clashed with coach Josh McDaniels and was summoned to NFL Commissioner Roger Goodell's office in New York.
Because of Marshall's legal record, he's one strike from a yearlong suspension. He was suspended for the 2008 opener following a series of disputes involving a former girlfriend. Last summer, he was suspended by the Broncos for throwing a tantrum at practice during training camp, when he was unhappy with his contract and with the team's medical staff.
But all that didn't dissuade Parcells, who had mixed results working with headline-making receivers Terry Glenn in New England, Keyshawn Johnson in New York and Terrell Owens in Dallas.
The Dolphins' Marshall plan is unknown, because the ever-secretive team didn't comment beyond issuing a brief news release. But he's their biggest addition since Venus and Serena Williams, who added glamour to the team's ownership group last year but failed to catch a single pass.
Miami's receiving corps wasn't too productive, either. The Dolphins had an NFL-low two touchdown passes of 20 yards or more last season.
Ted Ginn Jr. has been a disappointment since Miami took him with the ninth overall pick in 2007, and La Canfora reported Tuesday that the team will try to trade the speedy wideout before the draft. Ginn and the Dolphins' other receivers -- Brian Hartline, Davone Bess and Greg Camarillo -- combined for just six touchdown catches last season while averaging 11.7 yards per catch.
"We need big playmakers," Dolphins general manager Jeff Ireland said in February. "We need players that make chunk yardage. We need players that score touchdowns. We need to get more production out of the wide receiver position."
Marshall provides production. Last season, he caught 101 passes, including an NFL-record 21 during a Dec. 13 loss at Indianapolis, for 1,120 yards and a career-high 10 touchdowns.
Shortly after arriving in South Florida, Marshall attended the Miami Heat-New Jersey Nets game Wednesday night, sitting courtside in a Florida Marlins cap. He declined interview requests.
A television crew ran up to Marshall during the first timeout after he and two acquaintances sat down across the court from the Heat bench, and a security guard was stationed nearby to keep away other potential questioners.
Marshall spent much of the first quarter typing into his cell phone and chatting with a spectator. He smiled broadly after a basket by the Heat's Dorell Wright midway through the opening half.
New Dolphins defensive coordinator Mike Nolan, who was with the Broncos last season, most likely played a role in Miami's decision to make the trade. It frees the Dolphins to use the No. 12 pick in the draft on the defensive front seven, where help also is sorely needed.
The Broncos, who pick 11th in the first round, have needs at linebacker and elsewhere, and they'll now likely address the receiver position in the draft, too. Marshall's departure leaves Jabar Gaffney, who had 54 catches for 732 yards and two TDs last season, as Denver's top receiver.
Before speaking at an asthma program at Denver North High School on Wednesday night, McDaniels suggested the trade gave both Marshall and the Broncos a fresh start.
"I'm pleased with how the whole thing went down," McDaniels said. "I'm happy and excited for Brandon to have an opportunity to do something that he's wanted to do. And I'm also excited about the opportunities that we're going to be presented here in the coming week with the draft and continuing to build our team and our roster the way that we want to do it.
"Again, this is something where the situation was what it was, and I think we worked it the best way that we could so that all of us could kind of get what we were looking for."
The trade of Marshall came three days after receiver Santonio Holmes was acquired by the Jets, the Dolphins' AFC East rivals. The division power Patriots have Randy Moss and Wes Welker, who's recovering from knee surgery.
The deal also earned three exclamation marks from Miami cornerback Sean Smith.
"We got B Marsh, thass my dude!!!" Smith tweeted.
Marshall is the Dolphins' biggest trade acquisition since running back Ricky Williams came to Miami in 2002 for four draft picks, including two first-rounders.
The Seattle Seahawks also were interested in Marshall, but they weren't willing to part with the sixth overall pick to sign him. They traded their second-rounder (40th overall) to the San Diego Chargers for quarterback Charlie Whitehurst.
The Associated Press contributed to this report.