Forest left O’Brien out of their Premier League squad as they expected the loan to be completed – but Rovers did not submit the paperwork in time.
“Lewis deserves this opportunity to play football,” said boss Steve Cooper.
An appeal by Blackburn to have the block on the signing lifted was rejected by the English Football League at the start of March, leaving O’Brien in limbo, unable to add to his 17 appearances for Forest.
The Colchester-born midfielder is, however, eligible to play overseas and has seized the chance to sign for the side in the United States.
O’Brien joined from the Terriers last summer, one of the influx of new signings made by Forest as they prepared for life in the Premier League.
“Everyone knows about his situation,” added Cooper. “Now he is able to go and get some games under his belt between now and the end of the season and it will be a real positive for him.”