The 16-member squad named Sunday has four changes from the team that lost to Pakistan by an innings and 44 runs in Rawalpindi.
Kusal Mendis frustrated Zimbabwe's hopes of a series-levelling win in Harare with a stubborn 116 not out as the second Test petered out to a draw.
Angelo Mathews scored an unbeaten double-century against Zimbabwe at Harare and Jason Gillespie sent him a congratulatory message, creating much mirth on the Internet.
Suranga Lakmal took four for 27 to set up Sri Lanka for a 10-wicket win over Zimbabwe in the first Test in Harare on Thursday.
Zimbabwe vs Sri Lanka: Zimbabwe last played a Test at home against the West Indies in October 2017.
Zimbabwe will now be able to participate in the ICC Men's U-19 World Cup in January 2020 and the ICC Super League later in 2020.
Hamilton Masakadza ended his 18-year international career with a blistering knock of 72 that included five sixes and four fours.
Zimbabwe vs Afghanistan: The win, Zimbabwe's first in the tournament after three successive losses, also ended Afghanistan's record 12-match winning streak in T20Is.
The tri-series kick-starts on September 13 with a game between Bangladesh and Zimbabwe at Shere Bangla National Stadium, Dhaka.
The International Cricket Council (ICC) suspended Zimbabwe in July over a failure to keep the sport free from government interference, putting the country's participation in multi-nation events in doubt.
Zimbabwe cricketers expressed their disappointment over ICC's decision to suspend Zimbabwe for the interference of government in its administration.
The suspension will see the ICC's funding to Zimbabwe Cricket frozen and representatives from the team not allowed to participate in any ICC events.
An interim committee to run cricket has been announced and will have David Ellman-Brown, Ahmed Ibrahim, Charlie Robertson, Cyprian Mandenge as its members.
Team India are scheduled to play 5 Tests, 9 ODIs, and 12 T20Is in 2019-20 home season.
Henry Olonga, a handy medium-pacer in his playing days, is also a singer of great promise.
Enock Ikope was banned by the Tribunal for 5 years in respect of each breach.
Zimbabwe's Brendan Taylor fought valiantly with his second century of the Test but Bangladesh won the final match by 218 runs.
Bangladesh reduced Zimbabwe to 76/2 at stumps on day four after Mahmudullah's unbeaten 101 helped them declare the second innings on 224/6.