The 22-year-old winger joined the Reds in the summer and has featured in nineteen games this season.
Prior to joining FC United, Logan had progressed through the Rochdale youth system and was promoted to their first team squad whilst still a youth team player.
He made his professional debut in October 2012 against Plymouth Argyle.
In 2014 he had loan spells at Stalybridge Celtic, Southport and Wrexham and in 2016/17 he joined Guiseley AFC and spent time on loan at FC Halifax Town.
Logan joins FC United`s other talented young players Lloyd Allinson, Sam Baird, Mike Jones, Steve Affleck and Kieran Glynn to sign contracts until May 2019.