Members of the EIS and FELA voted by 96% to 4% to accept the offer, which was negotiated through the National Joint Negotiating Committee (NJNC).
They had first voted for industrial action in December 2015 and about 4,000 lecturers went on strike in March.
Lecturers said pay varied by up to Â£10,000 a year at different colleges.
EIS General Secretary Larry Flanagan said: "Members in colleges across Scotland have given their overwhelming approval of the pay offer.
"This pay agreement shows what can be achieved by a group of employees standing together, through their union, to protect their rights."
John Kelly, President of EIS-FELA said: "While this very clear ballot result settles this particular issue over pay, specifically the top of the salary scale for unpromoted lecturers across Scotland, there is still much work to do to agree the detail of all national pay scales.
"We are hopeful that constructive negotiations can move the process forward, so that further industrial action is not necessary in the future."
Further education college lecturers have approved a national pay offer in a trade union ballot after months of dispute.