Washington gave the Eagles a second-round pick in this year's draft and another conditional pick, either a third or fourth-round pick in 2011, in order to nab the 11-year veteran who had spent his entire career in Philadelphia.
"That was a tough decision to make," Eagles coach Andy Reid told a news conference. "He's been such a great player here for 11 years, set every record that you can set.
"Unfortunately things like this happen in the National Football League."
McNabb, 33, is likely to take over the Washington offence in place of Jason Campbell, who has been inconsistent and could only guide the Redskins to a 4-12 record last season.
The Redskins, like the Eagles, are in the NFC East and the teams will meet twice during the 2010 season.
"As far was Washington goes, we thought this was best for Donovan," said Reid.
"Obviously the compensation was right ... I will always wish Donovan the best of luck with the exception for two weeks during the year."
Reid said Kevin Kolb, a three-year veteran with 79 completions in just 130 attempts, would be the Eagles' new starter.
"Obviously we have a lot of confidence in Kevin Kolb to make this decision," said Reid.
McNabb had been the subject of trade speculation after the Eagles finished 11-5 last season but failed to advance past the first round of playoffs.
His time in Philadelphia was marked by deep runs into the playoffs only to fall short as he guided the franchise to five NFC championship games and one Super Bowl appearance.
Reid said the trade "was tough" on him, the front office and the rest of the coaching staff.
"I was very close with Donovan," he said. "And I'll remain close with Donovan. That part won't change. You can't erase the last 11 years."
(Reporting by Jahmal Corner in Los Angeles and Steve Ginsburg in Indianapolis; Editing by Greg Stutchbury)