The Democratic chairman will be authorized to issue subpoenas, a change from the commission proposal.
Cheney said in a statement the committee should issue subpoenas promptly and hire skilled staffers.
The move came after the Senate last month blocked creation of a commission approved by the full Congress. No Senate vote is needed to create a House committee. Most Republicans opposed creating a commission or special committee, arguing it would be used as a political weapon in next year's election.
The House approved the committee on a 222-190 vote.
"It will find the truth, which clearly the Republicans fear," said House Speaker Nancy Pelosi, D-Calif., who called herself heartbroken about the Senate blocking a commission similar to the one that studied the terrorist attacks of Sept. 11, 2001. "It does not appear at this time that we can have a bipartisan commission. Hopefully that could still happen. But in the meantime, we will have a select committee."