Clarke had signalled his desire to take on the role when Gill announced that he was stepping down last year.
At one point Clarke could have been elected unopposed, but Martin stepped up to provide competition.
However, the vote proved relatively comfortable for the 51-year-old, who has been in his current FA role since 2016.
Clarke is a former chairman and director of Leicester City and also worked as chairman of the Football League from 2010 until just before his FA appointment was confirmed.
The eight FIFA vice-presidents earn annual salaries of £190,000 during their four-year terms.