The 23-year old midfielder initially joined the Jags on loan in February 2012 before signing permanently from Hibernian in May that year and helped the club gain promotion to the Scottish Premier League last season.
Welsh was thrilled to commit himself to Partick: "I don't think we could have asked for a better start to the season and the great thing is that the players are really enjoying it.
"The gaffer has done a great job getting so many of last year's squad signed up on lengthy deals and I am glad to have sorted out one for myself.
"He has also added a lot of quality among the new faces so we know that we have to play well to keep our places in the team. It is early days but we are pleased with the start that we have made."