
The 33-year-old frontman, who has netted exactly 100 goals in 358 senior appearances, signed ahead of the Christmas and New Year period and could make his Pilgrims’ debut against Eastwood Town on Boxing Day.
Constantine, who scored eight times in 26 appearances for York City last season in the Blue Square Bet Premier, has spent brief spells with Braintree Town, Lewes and Tooting and Mitcham United this season, but is now in the process of relocating to Peterborough — and has chosen to link up with the Pilgrims.
Constantine’s professional career began in 2000 at Millwall and he has represented a variety of clubs since — culminating in a move to Leeds United in 2007.
His most prolific scoring spells arrived in stints with Southend United and Port Vale.
United co-boss Lee Canoville was delighted to see Constantine put pen-to-paper to complete his switch to The Jakemans Stadium.
Canoville told bufc.co.uk: “Leon is a big presence and a proven goalscorer throughout his career. It has taken some time to get him onboard, but we are delighted that he has agreed to join us.
“His experience will be invaluable in and around the younger lads at the top end of the pitch and we look forward to working with him.”