The former Wolves boss was identified as the first choice to replace Sean Dyche, who was sacked following Wednesday's goalless Premier League draw with the Molineux club.
Talks progressed swiftly and the two parties have agreed a contract, it's understood, with the deal set to be announced soon.
Pereira had been out of work since leaving Wolves in November after a disastrous start to the campaign.
But he kept them up the season before after taking over from Gary O'Neil and he has worked under Forest owner Evangelos Marinakis at Olympiacos.
Unless there are any unexpected late hitches, the Portuguese will be in charge for next week's Europa League play-off first leg at Fenerbahce.
But his first brief will be to keep Forest in the Premier League as they sit three points above the relegation zone with 12 games to go.
Dyche was in charge for 114 days and follows Nuno Espirito Santo and Ange Postecoglou out of the door in a tumultuous season at the City Ground.
Dyche left on the back of a run of just two wins from the last 10 league games, and taking two points from matches against Crystal Palace, Leeds and Wolves proved fatal.
It was supposed to be a memorable season for Forest after Nuno guided them to their first European qualification in 20 years.
He signed a new three-year Reds deal in June 2025, but was sacked in September following a breakdown in his relationship with Marinakis and sporting director Edu.
Former Tottenham boss Postecoglou was swiftly brought in as the Portuguese's replacement, but lasted only 40 days in the job, with Marinakis wielding the axe again within minutes of a 3-0 defeat by Chelsea.
