Deputy First Minister Nicola Sturgeon said the additional places would provide "high quality training" in key areas where skills are in demand and would help young people into work.
Jobless young people will be able to get training, along with those who face difficulties finding work, while those who want to learn new skills could be offered retraining.
The new college places are being created on courses for key sectors of the economy where skilled workers are in demand, such as the energy industry, the food and drink sector, health and the digital media.
Funding for the places is coming from the Scottish Government, via the Scottish Funding Council's Skills for a Competitive Workforce project, and the European Social Fund.
It comes after figures released last month showed colleges had seen student numbers drop by 140,000 in the last five years.
There were a total of 238,805 students at colleges in 2012-13, down from 379,233 in 2007-08. The fall came after colleges were told to prioritise courses that would improve people's chances of finding work, and reduce the number of people on short courses and leisure classes.
Ms Sturgeon announced the new places were being created as she visited West College in Paisley, where she met three students on a construction course.
The Deputy First Minister said: "This funding will provide high-quality training in areas where skills are in particular demand, and will help many young people into work. It will also provide retraining to workers so that they can develop their existing skills.
"To secure sustained economic growth, Scotland needs to have a skilled and adaptable workforce. It is this type of joint investment that will help us meet this ambition.
"By investing in the development of skills in key growth areas now, we can help drive Scotland's economy in the future. Scotland's colleges, now fully focused on supporting young people towards work, have a key role to play in this work."
Laurence Howells, interim chief executive of the Scottish Funding Council, said: "This is great news for learners and I'm proud the Funding Council has been able to play a pivotal role in securing this investment. Across Scotland's new college regions this means better life chances for young people, vital support for employers and better prospects for Scotland's economy."
Both students and teaching unions welcomed the announcement, with Larry Flanagan, general secretary of the EIS teaching union, saying: "Additional investment in education is always welcome and brings long-lasting benefits for Scotland's economy.
"The planned injection of an additional £13 million in funding into the further education sector will open up new opportunities for learners across Scotland."
Gordon Maloney, president of the National Union of Students Scotland, said: "These extra places will go a long way to boosting the number of opportunities available to gain skills in college, reduce unemployment and, if targeted right, ensure we protect access to education for those groups who stand to benefit the most."
Liz Connolly, vice-principal at West College Scotland, said she was "delighted" by the news, adding: "We will use this additional funding to support our employability activity, especially for 16 to 19-year-olds. In particular, we will be looking for opportunities to invest in some of the key growth sectors of the Scottish economy - renewable energy, creative industries, and food and drink."