The Republic of Ireland midfielder will spend the rest of the season with the Championship promotion hopefuls.
The Hawthorns move is just Molumby’s latest spell away from the AmEx.
He spent the 2019-20 season with Millwall, and the second half of last season at Preston.
The 22-year old looked set for another season with Brighton’s U23 side, before being afforded the chance to link up with international teammates Dara O’Shea and Callum Robinson.
New West Brom manager Valerian Ismael is delighted with his new signing, saying, “Jayson is the perfect example of a player who has the right mentality and suits our philosophy.
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“He is the right player for us and we are delighted to have him.
“His skills out of possession are incredible and he gives us more volume and more possibilities in midfield, which will support us with our intensity and this is one of his strengths.
“Jayson is young but he already has a lot of experience in the Championship and with Ireland. He has the perfect profile – our new profile – to be a West Brom player and I’m delighted to have him.”
Molumby looks set to win his 10th Republic of Ireland cap next week, after being named in Stephen Kenny’s squad for the World Cup qualifiers with Portugal, Azerbaijan and Serbia.