Meekin is no stranger to the Lions having spent time on loan at the club in 2010, making nine appearances.
He joined the Centurions from amateur side Leigh East in 2006 and made 23 appearances for the first team in 2009.
The prop has spent time on loan at Rochdale this season, but he now joins up with the Lions, replacing Johnson who departed the club last week due to work commitments.
A statement on the club website added: “Director of Rugby Paul Kidd is delighted to have Meekin on board as the former Leigh man looks for regular first team rugby and is keen to impress coach Steve McCormack.”
Unbeaten Swinton sit top of Championship 1 after eight games, dropping their first points of the season in a 22-22 draw against Whitehaven at the weekend.