A team spokesman said the six-foot-four, 275-pound native of Windsor, Ont., signed a rookie deal with the Cowboys on Wednesday.
Contract details were not immediately available.
The official announcement of the move comes a day after a report surfaced saying that Crawford had signed a multi-year contract with Dallas.
The Cowboys selected Crawford in the third round, No. 81 overall, in this year's NFL draft.
Crawford had 13.5 sacks and 27 tackles for a loss over two seasons at Boise State.
Most of that production came last year, when he registered 11 sacks and 13.5 tackles for a loss as a senior.