The Patriots announced the trade Tuesday, saying only that Branch was exchanged for an undisclosed draft choice.
ESPN.com first reported the deal.
"(He's) excited as can be," Branch's agent, Jason Chayut, said Monday night.
Carroll added that he expected Branch to be with the team at its next practice Wednesday.
"At this point, I do, yes," Carroll said of Branch being around later in the week.
Obviously, that won't be the case.
Branch was in Louisville, Ky., this weekend and had his number retired by the University of Louisville, where he played college football. He told the Louisville Courier-Journal that he was trying not to focus on trade rumors.
"I'm going to leave that to the people that handle that," Branch told the newspaper. "Right now I'm still a Seattle Seahawk, and whatever happens happens."
What happened was Branch being shipped back to New England. Reports of talks between the Seahawks and Patriots first surfaced last week following New England's trade of wide receiver Randy Moss to the Minnesota Vikings. The Patriots received a 2011 third-round pick and a 2012 seventh-round selection in that deal, a league source told NFL Network insider Michael Lombardi.
Branch is signed through next season. He is scheduled to make $5.45 million in base salary this year and $5.95 million in 2011.
Before coming to Seattle, Branch was a rising star in New England. He caught a career-best 78 passes for nearly 1,000 yards and five touchdowns in 2005, and that followed his Super Bowl MVP performance one season earlier. Branch had 11 catches for 133 yards in Super Bowl XXXIX against the Philadelphia Eagles.
Branch arrived in Seattle in 2006, acquired from New England in exchange for a first-round pick, but that first season with the Seahawks was the only time Branch was able to stay healthy. His career in Seattle was mostly defined by injuries, as he missed parts of the 2007, 2008 and 2009 seasons with some sort of ailment.
Most of Branch's injury problems revolved around his left knee, which he first hurt during a snowy playoff game against the Green Bay Packers in January 2008. He also missed time with hamstring and foot injuries.
Branch's future with Seattle was brought into question when the team signed Brandon Stokley. Just a few days after being signed, Stokley led the team in catches and targets in their loss at St. Louis.
The Associated Press contributed to this report.