The 23-year-old joined Blackpool back in July but has made just seven appearances this term, without scoring, due to a foot problem.
Grant, who has also played for the likes of Rochdale and Accrington, bolsters the Cod Army's attacking options, with David Ball currently sidelined due to an ankle problem.
"He is a very good player and we made enquiries to bring Bobby in last season," boss Graham Alexander told Fleetwood's official website.
"At the time Bobby had an offer from a Championship club so we fully understood why he chose his move.
"We heard Bobby might be available once again a couple of weeks ago but he has had a small injury so we had to wait until he was fully fit.
"He played in a reserve game earlier this week and we watched him play and he seemed fine. We have got a very good player on board.
"Bobby brings goals, he brings character and he brings personality. He wants to win and he is a very confident lad.
"He will be a great boost for the rest of the squad and they know that another good player has joined the ranks."