The youngster featured for the club's under-21 side as a trialist in a 1-0 defeat to Crystal Palace, confirm independent Ipswich website TWTD.
Fanimo is 21, and was released by West Ham on deadline day, in order to allow him to pursue his career elsewhere after failing to make the first team.
He shot to fame last summer after posting a GPS data sheet to his Twitter account detailing his in-game pace, which showed he was faster than Theo Walcott and Gareth Bale, as reported by The Metro, who dubbed him the fastest player in football.
Another West Ham youngster Blair Turgott was released on the same day as Fanimo and was immediately snapped up by League One side Coventry City, the BBC reported.
There's a particular reason Fanimo is coveted by Ipswich, as he netted four times against them for the Hammers' under-21s in one game a year ago.
Mick McCarthy's side are flying high in the Championship, currently occupying a play-off spot, and if all goes to plan for Fanimo and he clinches a permanent deal, he could be playing against them in the Premier League next season.
Ipswich signed another former Hammer as a free agent earlier in the season, Jack Collison, but struggles with injuries meant his short-term deal was not renewed and he signed instead with Bournemouth.