The team announced that the deals were completed but did not reveal contract terms.
According to ESPN's Adrian Wojnarowski, Bullock landed to a two-year, $8.2 million deal with a team option for the second season. The two sides initially agreed to a two-year, $21 million pact, but unspecified medical issues forced them to rework the numbers, per Wojnarowski.
Morris' deal is for one year and $15 million, according to multiple reports.
"With Reggie and Marcus, we are adding two more versatile, hard-nosed and accomplished players to an already improved roster," Knicks general manager Scott Perry said in a press release. "We value both players' perimeter shooting ability and their strong presence on the court and in the locker room. We're excited to have them in New York and are confident they will excel playing for this team under Coach (David) Fizdale."
Bullock, 28, averaged 11.3 points in 63 games (60 starts) last season, split between the Detroit Pistons (44 games) and the Los Angeles Lakers (19). He has a career average of 6.8 points over 272 games (119 starts) in six NBA seasons.
Morris spent the past two seasons with the Boston Celtics and averaged 13.9 points and 6.1 rebounds in 75 games (53 starts) in the 2018-19 season.
He originally agreed to join the San Antonio Spurs this offseason but changed his mind, choosing the Knicks instead.
Morris, 29, has career averages of 11.5 points and 4.6 rebounds in 545 games (292 starts) over eight NBA seasons.
--Field Level Media