Barrow made a positive start to the Premier League campaign for the Swans last season, firstly under Francesco Guidolin and then Bob Bradley, but fell out of favour when current boss Paul Clement joined the club in January.
The Gambia international has plenty of exerience in the Championship, having spent time on loan at Nottingham Forest, Blackburn Rovers and Leeds.
Reading manager Jaap Stam said: "I'm very pleased to welcome Mo to Reading Football Club and I'm delighted that we have been able to add another player to our squad ahead of the start of the new season.
"Now all our focus is on the challenge that lies ahead on Saturday and our trip to QPR."
Reading chief executive Ron Gourlay added: "We are delighted to have finalised a deal to bring Mo to Madejski Stadium.
"A lot of hard work is ongoing to try and strengthen Jaap's squad for the challenges of the season ahead and give us the best possible chance of enjoying another successful year.
"So I'm pleased that a player of Mo's calibre has opted to join us at Reading to try to help us achieve our goals."
Reading start their Championship campaign against Queens Park Rangers on Saturday.