Coach Dick Jauron made the announcement Wednesday, but wouldn't commit to a full-time starter beyond this weekend. Edwards, a rookie third-round draft pick, has gone 1-1 starting in place of Losman, who has resumed practice and appeared ready to return after spraining his left knee.
"(Edwards) is our starting quarterback this week, and we'll move on from there," Jauron said.
Jauron sidestepped when asked whether Losman has the ability to be the team's starter, saying instead: "I like our young quarterbacks. I think we've got a couple of real good quarterbacks."
And the coach refused to discuss the future.
"We're just talking about this week, fellas, and we're not going to talk about anything beyond it," Jauron said. "I don't mind you asking the questions in a lot of different ways, but we can save some time here because I'm just going to answer it this one way."
Jauron added that Losman was still rusty, and said he wanted more continuity because Edwards started the past two games.
Jauron said he consulted with his coaches, general manager Marv Levy and team owner Ralph Wilson, but maintained the final decision was his.
Losman is healthy enough to serve as the backup against Baltimore.
The Bills (1-4) are coming off their bye week and trying to rebound from a 25-24 loss to Dallas that saw Buffalo squander an eight-point lead in the final 20 seconds.
Losman has been out since he was hurt during the first series of a 38-7 loss at New England in Week 3. He said after practice he feels healthy enough to play, but accepted Jauron's decision to sit him out for at least one more week.
That doesn't mean he's ready to give up the starting job.
"Would I like to get another shot? Of course. Do I feel I deserve another shot? Of course. I've been through a lot with this organization throughout the years," Losman said. "I earned it a little bit to go in there and get a second chance."