Welbeck, 35, scored 14 goals in 40 appearances in all competitions for Brighton last term and will join Xabi Alonso's squad on the club's current pre-season tour.
"I'm really honoured to come to a club of this stature at what feels like a really exciting time. I know a few of the boys already and I've had fantastic conversations with the manager and already feel that connection," Welbeck said in a statement.
"I've got that fire in my belly and I'm ready to give it everything for this club to make everyone at Chelsea, and the supporters, proud."
The former Manchester United and Arsenal forward arrives at Stamford Bridge with 400 Premier League appearances to his name.
A product of United's academy, Welbeck broke into the first team in 2008 and won the Premier League title under Sir Alex Ferguson, as well as two League Cups.
He joined Arsenal in 2014, scoring 32 goals in 126 appearances across all competitions during a five-year spell before a season at Watford and moving to Brighton in 2020.
Welbeck scored 16 goals for England during an international career spanning eight years.
Meanwhile, Premier Leagers Brentford have signed Mali midfielder Mamadou Sangare on a five-year deal from French club RC Lens.
Sangare left Austria's Rapid Vienna to join Lens last year, and featured prominently as they won the French Cup for the first time and finished second in Ligue 1.
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