The 28 year-old joins the Swans on a season-long loan.
Benson was cleared to make the move on Tuesday after initial doubts over the transfer's paperwork on deadline day was cleared.
Swans boss Alan Sheehan said: "Manuel is a very exciting player who brings a lot of quality, energy and work-rate on and off the ball.
"He has Championship experience and has been a key performer at this level. We look forward to working with him and to Manuel making an impact in a Swansea shirt."
Director of football Richard Montague said: "Manuel's record shows he is a player who can make things happen, and we believe his speed and creative spark can be a real asset for Swansea City.
"He will add real dynamism to our play in the final third and we cannot wait for him to link up with his new teammates at Fairwood. Once we were aware this loan was a possibility we moved decisively to secure his services."