The 33-year-old Suryakumar will lead a 15-member T20 squad to tour Sri Lanka for three internationals starting on July 27 in Pallekele
Shubman Gill recently led a second-string Indian side to a 4-1 T20 series victory in Zimbabwe and has been named vice-captain in T20 and ODI matches.
Rohit will continue to lead the ODI team, which will follow the T20 side by taking on Sri Lanka in three matches on August 2, 4 and 7 at Colombo's R. Premadasa Stadium.
Virat Kohli will also return for the 50-over matches, while pace spearhead Jasprit Bumrah remains absent from the tour after a gruelling season.
Rohit and Kohli had decided to take a break but returned for the ODI matches as India begin preparations for next year's Champions Trophy to be hosted by Pakistan.
All-rounder Hardik Pandya, who was Rohit's deputy in the T20 World Cup, had started as a frontrunner for the job but lost out due to his frequent injury breakdowns.
Pandya, 30, suffered an ankle injury during the ODI World Cup at home last year and was out of action until the start of this season's Indian Premier League where he returned to captain Mumbai Indians.
Pandya remains part of the T20 squad but is out of the ODI series, which will see the return of Shreyas Iyer, who earlier lost out on his contract with the Board of Control for Cricket in India (BCCI).
Suryakumar, an attacking middle-order batsman who has been India's go-to player in the T20 format, remained new coach Gautam Gambhir's top choice, according to media reports.
Rohit, Kohli and Ravindra Jadeja announced their retirements from the T20 format after India's thrilling win over South Africa in the final last month in Barbados.
The match was also Rahul Dravid's last as head coach and Gambhir was handed the job last week to build on the team's World Cup win.
Suryakumar, who previously captained Mumbai in domestic cricket, last year led India to a 4-1 T20 series win over Australia and followed it up with a 1-1 result in South Africa.
T20I squad: Suryakumar Yadav (capt), Shubman Gill (vice-capt), Yashasvi Jaiswal, Rinku Singh, Riyan Parag, Rishabh Pant (wk), Sanju Samson (wk), Hardik Pandya, Shivam Dube, Axar Patel, Washington Sundar, Ravi Bishnoi, Arshdeep Singh, Khaleel Ahmed, Mohammed Siraj
ODI squad: Rohit Sharma (capt), Shubman Gill (vice-capt), Virat Kohli, KL Rahul (wk), Rishabh Pant (wk), Shreyas Iyer, Shivam Dube, Kuldeep Yadav, Mohammed Siraj, Washington Sundar, Arshdeep Singh, Riyan Parag, Axar Patel, Khaleel Ahmed, Harshit Rana
