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."

In spite of a sales uptick, the firm on Tuesday said net earnings fell 15% to $763m (Â£595m) from $898m in the same period last year.
The firm also lowered its profit guidelines for the year.
The stock price fell on the news, dipping about 3% in early trading on Tuesday.
Lockheed has come under pressure for its F-35 fighter jet program, which has been plagued by delays and cost overruns.
A report from the US government's auditing arm, the Government Accountability Office, on Monday found that "cascading delays" meant the cost of the programme would run more than $1bn over budget.
US President Donald Trump has also targeted the programme, tweeting in December that it was "out of control." He claimed that negotiations would lead to billions in savings.
Lockheed Martin shares suffer after Trump F-35 tweet
US to buy more F-35 fighter jets from Lockheed Martin
But chief financial officer Bruce Tanner said on a call with analysts that nothing significant had changed to the programme in the last six months, though talk about F-35 costs was "bundled" with pricing for some of the firm's other contracts.
Chief executive Marillyn Hewson said Lockheed profits took a hit this quarter on a defence programme for an international customer.
Lockheed also reduced the value of a joint venture in the Middle East, which is not seeing as much demand as expected.
But she said a "volatile" international environment suggests that military spending may increase, including in the US.
Lockheed sales in the first quarter were up 6.6%, to $11.1bn, from the same period in 2016.
"We remain hopeful that progress will continue to be made in this area and upcoming legislation will include the increases necessary to equip and maintain our fighting forces," she said.

Reports in the Netherlands say ex-Manchester United defender Jaap Stam, who recently left his role as a coach at Ajax, is a contender for the job.
McDermott, 55, returned to the Madejski Stadium in December for his second spell as boss of the Royals.
But he only won nine of his 30 games in charge and the Berkshire side finished 17th in the second tier.
A club statement said it had been a "difficult decision" for the board of directors to relieve McDermott of his duties.
Reading said they would now undertake a "rigorous recruitment process" in order to identify the former Arsenal midfielder's successor.
McDermott led the Royals to promotion to the Premier League in 2011-12, but he left the club in March 2013 after just over three years in charge.
Reading had also enjoyed considerable cup success under McDermott, reaching the FA Cup quarter-finals in 2010 and 2011.
He agreed a two-and-a-half-year deal on his return to the club in December and again led the Royals to the last eight of the FA Cup, where they were beaten by Crystal Palace.
Reading lost six of their final seven Championship games this season and finished the campaign 12 points above the relegation zone.
Further education college lecturers have approved a national pay offer in a trade union ballot after months of dispute.
[NEXT_CONCEPT]
Unexpected losses related to international business dragged down first-quarter profits at US defence giant Lockheed Martin.
[NEXT_CONCEPT]
Championship side Reading have sacked manager Brian McDermott after just over five months in charge.