The Express & Star revealed earlier this week that the midfielder was going to join the Baggies once he had put pen to paper on a new long-term deal at Stamford Bridge.
The 20-year-old is a player who has been on Albion's radar for a number of years following his impressive performances for Chelsea’s youth sides.
But last season saw him take that form into senior football after successful loan stints in the Championship at both Charlton and Swansea.
It is understood as many as 12 clubs have enquired about signing Gallagher on loan this season.
But the England under-21 international chose to join Albion with a phone call between Bilic and Frank Lampard key to the deal.
The two managers previously played alongside each other at West Ham.
"We’re delighted," Bilic said.
"I know the player from the Championship last season. He made a huge impact, first at Charlton and then Swansea.
"We were there – it’s not like somebody has told us ‘it’s a difficult league and there’s a player there’ - we were there.
"There was a chance in January we might’ve taken him before he went to Swansea, but it was very difficult and we couldn’t do it.
"When we saw the opportunity, we did it straight away. I have to thank Frank Lampard - I phoned him, he’s a top man. We’ve known each other since West Ham.
"He helped us with that, but the boy wanted to come.
"He’s ready to make the next step in his career and he’ll give us something we don’t have, that dynamic in the midfield.
"I’m expecting a lot from him. It’s a new level for him; we’re going to help him, he’s going to help us.
"Hopefully it’ll be an exciting and pleasant journey."