The 24-year-old Wales international has put pen to paper on a four-and-a-half year deal and will wear the Eagles’ No. 11 shirt.
Johnson will be eligible to make his Palace debut against Newcastle United at St. James’ Park on Sunday afternoon.
Boasting an eye for goal and pace to burn, Nottingham-born Johnson’s 19 goals saw him named Championship Young Player of the Season in Forest’s 2021/22 promotion-winning season. He then hit double figures in his debut Premier League campaign.
Johnson’s impressive performances earned him a switch to North London, where he enjoyed a productive spell at Spurs, finishing as their top scorer last season with 18 goals – including the match-winner in last season’s UEFA Europa League final against Manchester United – alongside seven assists.
At international level, Johnson has already won 42 senior caps for Wales, scoring on seven occasions, and represented his country at the 2022 FIFA World Cup finals.
Chairman Steve Parish said: “I’m delighted that Brennan has joined us at Crystal Palace – an exciting young talent with an excellent recent record in domestic, continental and international football.
“We feel we are the perfect place for Brennan to continue his already impressive journey, and his arrival bolsters our attacking options in what is proving our busiest season to date, competing on numerous fronts including, for the first time, in Europe.”
Manager Oliver Glasner said: "I’m really delighted that Brennan has joined the club. He arrives very early in the window, so credit to the club for making this happen so quickly.
"Brennan will give us options in our attacking play with his pace and goalscoring ability and with all the upcoming games he will be a valuable addition to the squad."
Johnson added: "I'm really excited and I'm really happy. Crystal Palace are such a great club, one that I've always admired.
"It's a great time for me to be here and join the journey that this club is on – I'm super excited."
Everyone at Palace would like to welcome Brennan to South London, and wish him the very best for his career in red and blue.