And yes, the motion was voted on in accordance with the FTPA; the Parliament has a detailed page on this question:
In order for the election to take place at least two-thirds of MPs had to agree to a motion in the House of Commons.
MPs approved the motion for an early general election by 522 to 13. The support of two-thirds of all MPs required for this motion to pass was reached.
MPs voted on the motion:
"That there shall be an early parliamentary general election."
Why do MPs need to vote on whether there will be a general election?
Under the Fixed-term Parliaments Act 2011, general elections are scheduled to take place every five years and the next general election was scheduled to take place on 7 May 2020. However, the Fixed-term Parliaments Act allows for an earlier election to take place:
if a motion for an early general election is agreed either by at least two-thirds of the whole House or without division
if a motion of no confidence is passed and no alternative government is confirmed by the Commons within 14 days.
At least two-thirds of the total number of MPs, 434 MPs, must vote for the motion to trigger an early general election. The motion could be passed without a division if there are no objections in the Chamber.