The two clubs have agreed the transfer fee with Hartson set so agree personal terms over the weekend.
The Celtic frontman is expected to sign a two-year contract with Bryan Robson keen to spearhead the Baggies back into the Premiership with a strikeforce of the former Welsh international and Nathan Ellington.
Hartson arrived at Parkhead in the summer of 2001 and has gone on to score 110 goals for the SPL Champions.