Khanna managed 192 votes to 200 garnered by Haggerty in a close second round while two other candidiates -- Juan Margets (ESP) and Rene Stammbach (SUI) were eliminated in the first round.
The election was held on the third and concluding day of the Annual General Meeting (AGM) of the world governing body of the game.
Haggerty will replace Francesco Ricci Bitti, who has decided to step down after 16 years in office.
The AGM also approved introduction of fifth-set tie break in the Davis Cup matches.
Khanna has always been critical of the way the current ATP set up works, saying it was heavily loaded in favour of only top-100 players, who are mostly from Europe.
Khanna is also President of Asian Tennis Federation (ATF) but his efforts to begin a closed circuit for the Asian players did not yield desired results.