The 20-year-old has signed a new five-year deal with Chelsea but immediately gone out on loan to the Baggies for the rest of this season.
The promising midfielder spent the first half of last season on loan at Charlton and the second half at Swansea, winning plenty of admirers for his performances in the Championship.
Aston Villa, Crystal Palace and Leeds have all been linked with a move for the England Under-21 international, but West Brom have won the race to take him on a short-term deal.
Bilic is thrilled with the move and has thanked his old West Ham teammate Lampard for helping to secure it.
‘We’re delighted,’ said Bilic. ‘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.
‘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 gonna help him, he’s going to help us. Hopefully it’ll be an exciting and pleasant journey.’
Bilic played at West Ham for a season-and-a-half in 1996-97, when Lampard was making early strides in his career.
West Brom take on Everton at Goodison Park on Saturday in the Premier League and Gallagher could go straight into the squad for the match.