The proposal will have to be approved by the Scottish Further Education Funding Council and by Jim Wallace, Lifelong Learning Minister. The target date for establishing the new institution, to be called Forth Valley College of Further and Higher Education, is August 1.
The new college will be the sixth largest in Scotland, with more than 20,000 students and 900 staff, behind James Watt, Aberdeen, Edinburgh's Telford, Dundee and the newly formed Glasgow Metropolitan.
"The aim is to benefit learners, communities and local employers as well as underpin financial viability and the development of buildings and facilities," Linda McKay, principal of Falkirk College, said.
John Taylor, principal of Alloa-based Clackmannan College, predicted "a bright new future" for college provision in the Forth Valley area, which mainly consists of Clackmannanshire, Falkirk and Stirling. The FE centre in Stirling was built in the last decade as part of Falkirk College.
A spokesman for the two boards said that they had both given an "absolute commitment" that a further education presence would be retained in these three main existing areas. But he suggested that there would also be increased demand for FE because of the projections for population growth in Stirling and Falkirk.
The merger is seen as having a particular benefit to Clackmannan College because of the physical constraints on its expansion, which has long been seen as a prohibiting factor in its development. Plans some years ago to move from the college's present site nearer to Alloa town centre were shelved, but could be revived under the merger.
The spokesman added: "While this is primarily about better provision in Forth Valley, it is true that the clearly sustainable, financially viable provision that the merger offers will be beneficial."
Following years of competition between colleges and the occasional flurry of unsuccessful attempts at merger, the Forth Valley plans represent the third move in this direction.
The creation of Glasgow Metropolitan College out of Glasgow College of Building and Printing and Glasgow College of Food Technology has already been approved and will come into effect officially on February 7.
Glenrothes and Fife colleges also aim to merge and, if the Lifelong Learning Minister gives his likely endorsement, that will take place in October.
There is also unfinished business among what were the "big three" colleges in Glasgow's Cathedral Street, following the decision by Central College of Commerce to pull out of merger talks with the colleges of Building and Printing and Food Technology. It is expected that Central College will reopen these discussions.