Cliftonville revealed they had accepted an offer from an unnamed club for the promising 19-year-old, who is due to join Northern Ireland's Under-21s for their upcoming games with San Marino and Germany.
It is understood he will be unveiled by Bremen before joining up with the Under-21 squad.
While Bremen have yet to confirm the deal, Cliftonville released a statement claiming terms had been agreed.
"The 19-year-old was subject to a transfer bid over the course of the weekend and, having undergone a medical and agreed terms with his new club, has this afternoon signed a contract to finalise the move," a Cliftonville club statement said.
Chairman Gerard Lawlor wished Boyce well as he joins the German side, who qualified for the Champions League group stages last week.
"(We are) disappointed as we are to lose a player of Liam's calibre, but we are delighted that he has been able to realise his dream of full-time football," he said.
"We are pleased, too, that the terms of the transfer are good for Cliftonville FC and naturally wish Liam the very best of luck in his future career.
"He has only been a part of the first-team picture for around a season and a half but made a highly significant contribution in that short time and leaves us with some great memories and, of course, our best wishes."