Bandara, 29, will leave for England with Kusal Perera, who replaced injured seamer Dhammika Prasad; both players will be available for selection for the Lord's Test, which starts from June 9.
"Bandara has been performing well domestically and he is the best choice available at the time for the English conditions," chief selector Sanath Jayasuriya said.
Sri Lanka will also wait for the results of tests on Shaminda Eranga's bowling action, which will take place on June 6. Eranga's action had been reported after the second Test, at Chester-Le-Street. If the tests conclude that Eranga's action is illegal, he will barred from bowling in international cricket with immediate effect.
Bandara was not in the preliminary squad for the tour, but leapfrogs Vishwa Fernando and Kasun Rajitha into the Test squad, thanks largely to his domestic experience. He was also the most successful seam bowler in this year's first-class tournament, taking 33 wickets at an average of 26.30 for Ports Authority Cricket Club. He has played 51 first-class matches in all, taking 141 wickets at an average of 29.85.