Welbeck and Watford came to a mutual agreement to terminate their association earlier this month after the Hornets’ relegation to the Championship.
Welbeck spent one season at Vicarage Road and made 20 appearances in all competitions, scoring three goals.
The 29-year-old came through the youth ranks at Manchester United and won one Premier League title at Old Trafford but left for Arsenal in the summer of 2014.
Welbeck won one FA Cup with Arsenal before joining Watford as a free agent when his contract with the Gunners expired in 2018.
He has signed a one-year contract at the Amex Stadium.
"We are delighted to have Danny joining us. He will complement our existing striking options," Brighton manager Graham Potter told the club's website.
"He's got an undoubted pedigree, and he is quick and technically very good. He will add to our attacking threat and we are thrilled to add another player of his experience and quality."
Brighton's technical director Dan Ashworth added: "I think Danny's arrival concludes what we feel has been a very good window for the club."
"A lot of planning, diligence and hard work went into the recruitment side, and I would like to thank all the club's different departments for their efforts in achieving that."
Welbeck will wear the number 18 jersey at his new club and will be eligible to make his debut on October 26 against West Bromwich Albion in the Premier League.
