India, who suffered a shock exit from the first stage of the World Cup, play a three-match one-day series followed by two Tests from May 10.
However Tendulkar and Ganguly retained their Test spots.
Out-of-form Delhi batsman Virender Sehwag made the one-day team but was dropped from the Test side.
Off-spinner Harbhajan Singh, left-arm seamer Irfan Pathan and pacer Ajit Agarkar, who had a miserable outing in the World Cup, were axed from both teams.
Bengal batsman Manoj Tiwary, 21, is the lone new face in the one-day team while 18-year-old U P leg spinner Piyush Chawla, who has played one Test, has been drafted into the one-day team following Anil Kumble's retirement. A clutch of younger players have been recalled. Left-arm paceman R P Singh, yet again, has been recalled in ODI squad.
The only debutant in the Test team was Baroda left-arm spinner Rajesh Pawar.
V V S Laxman and Wasim Jaffer retained their places in the Test squad along with Anil Kumble who had recently announced his retirement from ODIs. Speaking to reporters after the meeting, Vengsarkar said Sachin and Sourav had been rested since India will play as many as 45 ODIs in the coming year, and ''this is the tour where we can try out youngsters''. He said he had personally spoken to the duo and both had accepted the reasoning of the selectors.
Vengsarkar said the selection committee felt that Harbhajan Singh had stagnated and has not done well in the past year and, therefore, was dropped from the squad.
Niranjan Shah, the secretary of the cricket Board and convenor of the selection committee meeting, said the selectors had been given in writing to select a young team, though the final selection was left totally to them.
Vengsarkar also did not find anything wrong in this and said that he and the selection committee had full freedom to choose the team based on the form and fitness of the players.
Vengsarkar said they had considered the name of Rohit Sharma, the young Mumbai batsman. ''He is an exciting prospect and would get his chance soon, but he was unlucky to miss this tour,'' the chairman added. To a question on retaining Sehwag in the one-day team, Vengsarkar said the Delhi batsman had found his form in West Indies and played well during the World Cup, therefore he retained his place.
The chairman also said that Dinesh Karthick has been chosen as a specialist opener for the Tests.
The Indian squads for both the ODIs and Tests will assemble in Kolkata on May 1 and will have a five-day camp from May 2 to 6, before flying off to Bangladesh on May 7 where they will play three ODIs beginning from May 10 and two Tests immediately after the ODIs.
Mr Shah also informed that they had called Pankaj Singh, Ranadeb Bose, Ishant Sharma and Yo Mahesh to bowl at the camp.
Team for ODIs: Rahul Dravid (captain), Gautam Gambhir, Robin Uthappa, Virender Sehwag, Yuvraj Singh, Mahendra Dhoni (wk), Dinesh Karthik (standby wk), Manoj Tiwary, Shanthakumaran Sreesanth, Munaf Patel, Zaheer Khan, Rudra Pratap Singh, Piyush Chawla, Ramesh Powar and Dinesh Mongia.
Team for Tests: Rahul Dravid (captain), Wasim Jaffer, Sachin Tendulkar, Vangipurappu Laxman, Mahendra Dhoni (wk), Sourav Ganguly, Yuvraj Singh, Dinesh Karthik (stand-by wk), Shanthakumaran Sreesanth, Zaheer Khan, Vikram Rajvir Singh, Munaf Patel, Anil Kumble, Ramesh Powar and Rajesh Pawar.
Coach cum Manager: Ravi Shastri. Bowling coach: B K Venkatesh Prasad. Fielding coach: Robin Singh (sr).
Tour Itinerary: One day internationals: May 10 and May 12 in Mirpur, May 15 in Chittagong. Tests: May 18-22 in Chittagong and May 25-29 in Mirpur.
ThatsCricket (with inputs from Agencies)