The 26-year-old - who played under Lennon at St Mirren - has signed an 18-month contract and becomes the Clyde's boss second signing of the January transfer window after the acquisition of Tom Lang.
Love started his career at St Mirren and has also had spells at Stenhousemuir (on loan), East Stirlingshire, Annan Athletic and Albion Rovers as well as Brechin.
He helped Albion Rovers win the League 2 title in 2014-15 and was part of the Brechin side who won promotion to the Championship last season..
Lennon said: "I was pleasantly surprised to hear that Ally was available and he was keen to be playing regular football again.
"I think for him to come out of the Championship and go to League 2 level, it had to be to a club like Clyde, with the infrastructure and the work that the board are doing behind the scenes. I also worked with Ally before at St. Mirren so he knows what I'm about and that was maybe a factor.
"He's a player that consistently gets goals and assists and that's something we need to add to our recent performances.
"He also works his socks off on the other side of the game and it doesn't surprise me that he has gone on to have success since leaving St. Mirren.".