The delegates were originally stripped because the two states violated party rules by holding primaries before Feb. 5. The delegates from each state were given half-votes at a contentious party meeting in May, as part of a compromise designed to give two important states some role at the convention.
Obama's former Democratic rival, Hillary Rodham Clinton, had won both primaries, though Obama's name was not on the Michigan ballot and neither candidate campaigned in Florida.
"I believe party unity calls for the delegates from Florida and Michigan to be able to participate fully alongside the delegates from the other states and territories," Obama said in the letter.
Some of Clinton's supporters were outraged that the delegates were not fully reinstated in May. They were also angry that Obama claimed some of the delegates won by Clinton in Michigan.
Party leaders in Michigan had developed a plan to award Obama delegates even though he wasn't on the ballot. Their plan served as the basis for the eventual compromise approved by the party's rules and bylaws committee.
Obama clinched the Democratic nomination three days later, and he has been working to win over Clinton's supporters ever since.
Florida has 211 delegates, including superdelegates, and Michigan has 156. Both states are expected to be contested in the November election.
Obama's endorsement virtually guarantees the delegates will have full voting rights. Clinton, who also has supporters on the credentials committee, had lobbied to reinstate the delegates.
The three co-chairs of the credentials committee issued a statement Sunday saying the issue of Florida and Michigan would be a "top priority" at their meeting.
"As always our goal is to ensure a fair process and a unified Democratic Party so that we can win in November," wrote Alexis Herman, James Roosevelt Jr. and Eliseo Roques-Arroyo.
Granting full voting rights to the delegates raises questions about whether the party will be able to control its own nominating process in the future.
Obama said he supported the party's efforts to control the primary calendar.
"As we prepare to come together in Denver, however, we must be - and will be - united in our determination to change the course of our nation," Obama said.
Both parties struggled to control their primary calendars this year, with states jockeying to increase their influence by moving their nominating contests earlier. The Republicans penalized five states for holding contests before Feb. 5, stripping them of half their delegates: Florida, Michigan, New Hampshire, Wyoming and South Carolina.
Republican presidential candidate John McCain has not publicly pressed for their reinstatement, though many GOP insiders expect them to have full voting rights as well.
The Democrats had stripped all the delegates from Florida and Michigan, and both Obama and Clinton agreed not to campaign in the states before their primaries, which were held in January. Obama and Clinton went on to wage a historic fight for the nomination, with Florida and Michigan on the sidelines until the outcome was decided.