Nelson, who serves on the Armed Services Committee, said he will vote for a compromise plan reached Monday by the White House and Democratic congressional leaders, CNN reported.
While the measure could come up for a vote by the committee and the full House as early as Thursday, the news network said, the men who lead the four military branches sent letters to Sen. John McCain, R-Ariz., and Rep. Buck McKeon, R-Calif., saying they oppose congressional action before a military review is completed.
The proposed deal would not repeal the "don't ask, don't tell" policy until after President Barack Obama, Defense Secretary Robert Gates and Adm. Mike Mullen, the Joint Chiefs of Staff chairman, certify the military review expected by the end of the year.
"I spoke to Secretary Gates and he advised that while he preferred waiting until the study is completed, he can live with this compromise," Nelson said in a statement.
Nelson said the compromise shows Congress "values the Pentagon's review that will include the advice and viewpoints from our men and women in uniform, from outside experts and from the American people about how to implement the repeal."
"It rests ultimate authority to make this change with our military leaders," Nelson said. "I believe this is the right thing to do."
A spokesman for Sen. Joe Lieberman, Ind-Conn., an author of the compromise, told CNN supporters were "increasingly confident" of it receiving committee approval.