The 24-year-old has been a key player for the Citizens, scoring 14 goals in his 97 appearances and winning the club’s Player of the Year prize for the 2019/20 season.
Henderson joined Hearts as a youth from Hutchison Vale in 2014 and spent time on loan at Preston Athletic and Stenhousemuir before making a permanent move to Falkirk in the summer of 2016.
He joined Cowdenbeath and Edinburgh City on loan from the Bairns before signing a permanent deal with City in January 2018. He spent time in Australia with Stirling Lions before rejoining City in August 2018.
Henderson struck five goals this term as the side reached the League One play-off final, losing to Dumbarton.
Red Lichties boss Dick Campbell said: “I’m delighted to secure the signature of Liam. He has all the attributes that I look for in an Arbroath player and is a fantastic addition to our team.”