In a statement released by the club, technical director Luke Dowling insists Shan has convinced the board Albion's 'best prospects for promotion lie with him overseeing the first team'.
The Baggies are planning to bring in one or two experienced coaches onto Shan's team in the next couple of days to help him see out the season.
It comes after managerial target Alex Neil signed a new three-year contract at Preston North End following heavy speculation he would be joining the Baggies.
But Shan has also impressed, delivering 12 points from his six games in charge and all-but cementing Albion's place in the play-offs, which looked under threat when he took over.
Dowling said: “Jimmy has fully earned this opportunity to take us through to the end of the campaign.
“He has earned the support and confidence of the players who have bought into the structural and organisational changes Jimmy has introduced. He has the backing of everyone to push on now and take us forward with momentum.
“Of course he recognises, as do we, that there is space for some more experience to join the coaching group and we expect to be able to clarify this element over the coming days.
“But Jimmy has impressed everyone with the way he has tackled the challenge.
"He is confident in his abilities, just as we have confidence in him, and he has convinced us all that our best prospects for promotion lie with him overseeing the first team.”
When Shan took over, the Baggies had not won a single game at The Hawthorns in 2019, but on Saturday he recorded his third home win in a row.
Until now, he has been operating under a game-by-game basis, unclear of how long he will remain in charge. But now there is some welcome clarity.
Shan said: “I’m happy that we can now move forward with clear planning and direction for the remainder of the season.
"It won’t change the work ethic and application of the players and the staff but it enables us to crack on with a clear target in our sights.
“From a personal point of view there is huge, huge pride to be given the responsibility. For me it is a chance to see the journey through that began at the end of last season.
“I’ve heard it said that with two or three extra games we may have stayed up last season. My aim is to make sure we get those extra games at the end of this season and complete our road back to the Premier League.”