The Bluebirds man has moved to the Scottish giants subject to international clearance.
Rangers have paid Barrow an undisclosed fee for his services.
Steven Gerrard worked alongside the 22-year-old when he was coming through the ranks at Anfield.
He left Liverpool in the summer of 2018 and joined Barrow and has made 18 first team appearances.
A statement on the club’s website confirmed the transfer.
“We thank Andy for all of his efforts in a Barrow shirt and wish him all the very best for the future,” it read.
Young goalkeeper Brad Wade has joined on a one month loan from Rochdale and is eligible for tomorrows trip to Chesterfield.