The deal was confirmed by the Barclays Premier League club in a statement on their official website.
Goodwillie, 22, has signed a four-year contract.
Blackburn did not disclose the transfer fee involved, however Goodwillie is believed to be costing Blackburn an initial ?£2million.
He was reportedly wanted by Blackpool and Cardiff before the battle for his services came down to a contest between Rangers and Blackburn.
Blackburn agreed a fee with United on Friday, and although Rangers made several efforts to strike a deal, they did not match their SPL rivals' demands.
The structure of payments was reported to have been a stumbling block for the Scottish champions.
Goodwillie underwent a medical with Blackburn on Tuesday and his arrival at Ewood Park will come as a fresh blow to Rangers, who have been knocked out by Malmo in the third qualifying round of the Champions League.
Blackburn said in their statement: "Rovers have seen off fierce competition from a host of other clubs to make their first signing of the summer."