India finished second in Group H behind hosts Saudi Arabia. The finals will be held in Jakarta next July.
Pakistan, who were set to host the tournament this year in the UAE, have exchanged hosting rights with Sri Lanka, who will stage next year's event, while the PCB will host the 2022 edition.
Defending a paltry total of 106, India dismissed Bangladesh for 101 in 33 overs, courtesy 18-year-old Ankolekar, who emerged as the star of the Indian team with figures of 5 for 28 from 8 overs.
Mendis made his debut against the West Indies in a one-dayer in April, 2008, but it was his remarkable haul of 6/13 against India in the Asia Cup final three months later that turned heads around the world.
Just a week back, the senior team beat Bangladesh in a closely fought final in Dubai to emerge as continental champions.
India, led by Rohit Sharma, pipped Bangladesh by three wickets off the last ball in the thrilling final to retain the title.
Rohit said Jadeja showed his burning desire to make a strong comeback and grabbed the opportunity with both hands after being sidelined from white ball cricket for close to 15 months.
In the absence of regular captain Virat Kohli, Rohit led India to their seventh Asia Cup title on Friday night, defeating Bangladesh in a last-ball thriller.
The team management as well as the national selectors would be worried about the shaky middle order with the World Cup only months away.
India secure the title for the seventh time in 14 editions.