Graham Dorrans has signed a two-year deal with Norwich City following a successful loan spell with the club.
Bournemouth have signed their second goalkeeper in two days by acquiring ex-Reading stopper Adam Federici.
Berahino, who has burst on to the scene this season with six goals in nine matches for Albion, is to put pen to paper on a new contract "in the next 24 hours" according to head coach Steve Clarke.
The 20-year-old striker, who grabbed the winner in a 2-1 victory over Manchester United at Old Trafford in September, has also bagged six goals in four games for England Under-21s.
After being constantly questioned about Berahino's new deal over a number of months, Clarke showed signs of relief when asked again on Thursday whether the matter was almost done and dusted.
Finally able to give a definitive answer, Clarke said: "I'm not very good at predictions, but I'm going to make another one - Saido will sign his contract in the next 24 hours."
Suggesting the deal would be a weight off Berahino's mind, Clarke added: "It will be great for Saido because he is a young boy who has maybe become a little bit distracted by the fact it has been ongoing for so long.
"I just feel there have been other things on his mind over the last couple of weeks.
"When you get so close to signing what I have described before as a very, very, very good contract, as a young boy it can be difficult sometimes to get your head around that.
"That's been a little negative with regard to the situation, but there are not too many negatives surrounding Saido this season.
"He has been a breath of fresh air in the squad, been a revelation. He's made a big contribution to us already.
"When he signs his contract he will have a massive part to play in the rest of the season for us."
Despite there being a number of quality forwards in the West Brom squad, Clarke has no qualms Berahino will continue to make an impact.
"Hopefully now he's going to sign we can forget talking about contracts and talk about Saido the player, and keep trying to help him improve," added Clarke.
"And he shouldn't be worried about where he is in the pecking order.
"I think I have shown this season if it's the right moment to put him on the pitch, I've done that, so he doesn't have to worry about that.
"He knows exactly where he is in the scheme of things here and how I use my squad.
"When I turn to my bench and I've choices to make Saido has shown he can be the player I bring on to the pitch, or he can start games."