The Croatian playmaker underwent a medical at Forest yesterday afternoon ahead of completing the loan move.
Krovinovic’s departure from The Hawthorns was widely expected this month, with boss Sam Allardyce having deemed him surplus to requirements.
The 25-year-old had initially been set to sign for Hajduk Split for the rest of the season, but instead has moved to Forest in the Championship.
Krovinovic made 40 appearances in the second tier while on loan with the Baggies last season, scoring three goals as they won promotion to the Premier League.
He then returned to the club in September, on the insistence of then boss Slaven Bilic, but started just five top-flight matches over the first half of the season.
Krovinovic’s only appearance under Allardyce, who replaced Bilic last month, came as a substitute in a 5-0 home defeat to Leeds.
Allardyce, meanwhile, has revealed he told Albion’s backroom team to up their standards shortly after his appointment as boss.
The survival specialist immediately appointed Sammy Lee as his No.2 before also adding Robbie Stockdale, who he worked with it Sunderland, and Baggies legend James Morrison to his backroom team. And he had a strong message for staff which he inherited.
“I have some great coaches here and backroom staff that are pulling the way I want them to pull,” the boss said.
“It has been a case of lifting everyone’s standards and that includes the backroom staff.
“I have asked the backroom staff to lift their own standards.
“The staff that work with me, who have always worked with me, know my standards anyway.
“But every staff member behind the scenes has been asked to lift their standards which helps lift the standards of the players.
“If they deliver a better service then the players get better quality and we get more capable of providing the players with the right information to go out and achieve a result.
“The players seem to have responded to that.”
Albion are not in action this weekend after being knocked out of the FA Cup by League One Blackpool.
But while Allardyce would still like to be in the competition, their exit means he will have had a full week to prepare for the visit of Manchester City on Tuesday.
Coronavirus together with the hectic festive schedule meant the 66-year-old wasn’t able to spend as much time on the training ground as he would have liked in the weeks after his arrival.
So he does feel another seven days – which they had in the build-up to the derby win over Wolves – will benefit his side.
“We have to face facts, there is no doubt the next game is massively difficult - against Manchester City,” he said.
“They are the top form team in the league and if we are to get a point like we did at their place, that would be magnificent.
“Man City will be difficult but having a week to prepare for it is a good thing for me.
“But there are two things in the week, one getting ready for Manchester City and one finding new players.
“After we finish with the players we will be hellbent, me and Luke (technical director Luke Dowling), on finding players to come in and help this squad get better.”