Shan has been placed in charge of Albion after their failed attempt for Alex Neil.
West Brom caretaker manager Jimmy Shan will remain in charge until the end of the season.
The 40-year-old has overseen four wins in six games since the Baggies sacked Darren Moore last month.
While there was never an official approach, Albion wanted Preston boss Alex Neil but the Scot signed a new three-year deal at Deepdale on Sunday.
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.”
Albion are fourth in the Sky Bet Championship and they remain on course for the play-offs with four games remaining after beating Neil’s Preston 4-1 at The Hawthorns on Saturday.
“Jimmy has fully earned this opportunity to take us through to the end of the campaign,” technical director Luke Dowling told the club’s website.
“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.”
Neil: ‘Speculation over future has affected players’