The 26-year-old joins the Scottish Premiership club as a free agent following his release from Norwegian side Tromso IL.
Fojut began his career with Bolton Wanderers before loan spells with Stockport County and Luton Town.
"I played in English football for five years and it was always my wish to play in the United Kingdom once more. This is a great club and I feel this will be an excellent move for me and my career," he told Dundee's official website.
"I look forward to helping United continue the progression it has shown over the last few years and I would like to win trophies for the fans."
United return to action on Wednesday when they face Forfar Athletic in a pre-season friendly.