After making 30 appearances for the Baggies, the Republic of Ireland international's fee is believed to be around £900,000.
The 22-year-old was unveiled via the club website which confirmed tying him down until 2025.
What has he offered
After joining in the summer, Molumby's time at West Brom has been marred by a disappointing season for the club as a whole.
Perched just inside the top half of the second tier table, the Baggies' season has unravelled spectacularly since their promising start to the campaign.
He had to wait until the 80th minute of their 1-0 defeat to Stoke City in October to make his first appearance for the club, but since has become an important member of the first-team squad.
Molumby showcased his busy and assertive attitude to the Baggies' faithful and gave them a glimmer of what the Irishman could offer in the future.
A deflected effort following a late-arriving run into the penalty area gave Albion the lead in an eventual 2-1 defeat to in-form Middlesbrough.
But it's arguably the defensive qualities that have left a section of The Hawthorns faithful optimistic about him staying permanently.
Molumby provides a tidy touch when screening the back-line, completing 721 accurate passes since his arrival at the club, meaning 75% of them find a target.
His tenacity and strong mental resilience arguably set him apart from the rest of the current playing squad, with a lack of mental strength being blamed for their poor form.
However, often banded in a midfield three under Bruce, alongside a combination of Alex Mowatt, Jake Livermore and Taylor Gardner-Hickman, there hasn't been enough creative flair for the Baggies in the middle of the park.
Often seen as too 'sideways' on the ball, Molumby has been partially blamed for a lack of progression in midfield.
Making just under 11 progressive passes per 100 balls played, the Capoquin-born general ranks significantly below the average Championship midfielder.
There's a feeling that if Molumby were to be paired with a more progressive midfield signing following the summer window, he may be able to complement them more effectively than the current crop of partners.
Steve Bruce on the signing
“We’re really pleased to have Jayson on board permanently," Bruce told the club's official website.
“He’s a young player full of energy and passion, and we see plenty of potential in him to grow and develop further.
“He’s only 22 and he’s already played more than 75 games in the Championship.
“He’s managed to force himself into our XI recently and now his challenge is to stay there by continuing to show improvements in his game.”