Russell, who was part of West Indies' victorious World T20 squad, will be available for four NatWest T20 Blast - home and away against Derbyshire, plus trips to Yorkshire and Worcestershire - before heading to the Caribbean Premier League.
"With his batting, bowling and fielding taken into consideration, Andre is one of the leading T20 players in the world right now, and he keeps proving it at big tournaments," Nottinghamshire director of cricket Mick Newell said. "Wayne Noon worked with him during the Big Bash League where the two of them struck up a good relationship, so we know he'll fit well into our dressing room."
Tahir, the South Africa legspinner, who had a brief spell with Nottinghamshire last season, will then join for the last seven matches of the group stage and is also expected to be available for six County Championship matches which will be a boost for Nottinghamshire who have won just one out of seven four-day games so far.
"We've seen many times how valuable a world class leg-spinner can be, in all formats of the game," Newell said. "Having him available will also allow us to make the most of some of the drier pitches in four day cricket at the back end of the summer.
"He can be a threat on any surface, but throw him the ball on something that's offering turn & bounce and he could be a real match winner for us at a pivotal point of the season."
Newell also said that Tahir will play a valuable mentoring role for the club's spinners, Samit Patel, Matthew Carter, Sam Wood and Connor Marshall.