Edwards is expected to sign a contract Wednesday morning and join his new teammates at practice later in the day.
The Jaguars waived linebacker Alvin Bowen to make roster room for Edwards, who receives a fresh start after things went south in Buffalo and provides Jacksonville with a viable option behind Garrard.
"Todd Bouman is a guy who knows our system, and he's here as our backup right now," Jaguars coach Jack Del Rio said Tuesday on Sirius NFL Radio's "Movin' the Chains" (via ProFootballTalk.com), "but to have a guy who has a chance to go forward beyond just next week and the rest of this season, but beyond that as a prospect, it's a little bit like adding a draft pick, and so we're excited to have him aboard."
Edwards started the first two games for the Bills this season, completing 29 of 52 passes for 241 yards and one touchdown. He also threw two interceptions and lost both games, prompting first-year coach Chan Gailey to turn to Ryan Fitzpatrick to spark an inept Buffalo offense.
"We're counting on there being a little bit of a learning curve," Del Rio said of Edwards learning the Jaguars' playbook. "He is a smart kid, he did go to Stanford, so we're thinking the learning curve maybe can be accelerated. But we'll do our best to get him caught up as quickly as possible."
Edwards could take over for Garrard, who threw four interceptions and was benched in a 25-point loss at San Diego on Sept. 18. He was even worse Sunday at home, completing just 13 of 30 passes for 105 yards with an interception in another 25-point loss, this time to the Philadelphia Eagles. He also was sacked six times and botched a pitch to running back Maurice Jones-Drew.
"We expect him to bounce back. We need him to bounce back," Del Rio said of Garrard. "Obviously, we can't function as a football team if we're playing that poorly in particular with our passing game."
Del Rio and Jaguars owner Wayne Weaver challenged Garrard in January. Del Rio called Garrard a "second-tier quarterback." Weaver said Garrard needed to be more accountable and spend more time working with the team's young receivers.
Garrard responded with what coaches and teammates called his best offseason. He even threw three TD passes in the season opener. But poor decisions, bad throws and costly turnovers have plagued him the last two weeks.
Garrard signed a six-year, $60 million extension in 2008. It was the richest contract in franchise history and included $18 million guaranteed. It also was a reward for 2007, when Garrard emerged as a legitimate starter, threw 18 TD passes with just three interceptions and led the Jaguars to their first postseason victory since 2000.
But Garrard has been mediocre since. He had 15 TD passes and 13 interceptions in 2008, and the Jaguars won five games. He had 15 TD passes and 10 interceptions last season, and the team won seven games. He was sacked 42 times in each season.
Edwards, a third-round draft pick by Buffalo in 2007, has thrown for 5,739 yards and 25 TDs with 27 interceptions in his career. He started 32 games for the Bills.
The Associated Press contributed to this report.