Vick and Nick Foles, who took over when Vick was injured last season, had been in competition for the starting quarterback slot.
"We've evaluated the situation and Michael Vick is going to start for us against the Washington Redskins," Kelly said. "I met with the quarterbacks this morning and they're all on board.
"[Vick is] our starter for the season. It's not a one-game trial basis."
Vick played in 10 games last season, missing time because of a concussion. He completed 58.1 percent of his passes for 2,362 yards, 12 touchdowns and 10 interceptions.
Foles, who was a rookie in 2012, played in seven games and started six. He threw for 1,699 yards, six touchdowns and five interceptions.
The Eagles went 4-12 on the season, costing Coach Andy Reid his job and creating a coaching vacancy eventually filled by Kelly, who coached at Oregon previously. Kelly said there would be an open competition for the starting quarterback spot.
"It was a healthy competition," Kelly said. "I think it made both players better. They both played at a high level, I just think Mike played a little better."
Vick, 33, is in his 10th season in the NFL. He started with Atlanta but was released by the Falcons after a conviction related to dog-fighting charges. After Vick served a prison term, he signed with the Eagles.
He's completed 1,626 of his 2,889 passes for 20,274 yards with 123 touchdowns and 82 interceptions in a 121-game career.
Philadelphia opens the 2013 season Sept. 9 at Washington.