It was confirmed in recent months that the 29-year-old would be leaving The Hawthorns upon the expiration of his contract in the West Midlands on June 30.
Once it was clear that the Baggies were unable to return to the Premier League, who remained keen on extending Johnstone's contract, the shot stopper confirmed that he would not be signing a new deal to extend his four-year stay with the club.
As a result, West Brom boss Steve Bruce left Johnstone out of the matchday squad for their final five games of the campaign, in which they finished in a disappointing position of 10th following their relegation from the top flight in 2020-21.
The likes of Tottenham Hotspur, West Ham United, Southampton and Fulham have been credited with an interest in signing the Manchester United academy product on a free transfer this summer, but journalist Nixon is reporting that Palace have won the race.
Eagles boss Patrick Vieira had been keen to provide competition for current goalkeepers Vicente Guaita and Jack Butland ahead of the 2022-23 campaign, and had prioritised Johnstone as his main target.
Johnstone is also said to be searching for a Premier League club that can guarantee him first-team football ahead of England's journey to the World Cup in Qatar at the end of the year.
The 29-year-old is keen to be a part of Gareth Southgate's squad for the tournament, having being part of the side that finished runners-up to Italy in the European Championships last summer, although Johnstone did not feature.
Johnstone leaves West Brom having played 167 appearances for the club across all competitions, whilst he also made three appearances for England during his time in the Black Country.