Abertay University, Dundee, will trial the new "fast track" degrees from September in seven subjects.
The degree courses will include exactly the same content as conventional studies, but with more working weeks in the second and third year allowing students to graduate in 2017 - 11 months ahead of their peers.
Market research by the university indicates strong support for the accelerated timetable, with students keen to get to the jobs market faster and burdened with lower levels of student debt.
In 2011, Dundee University become the first institution in Scotland to offer a three-year honours degree to students from Scotland and the rest of the UK. The institution argued the move significantly reduced the total cost of a degree once living costs such as accommodation are factored in.
In 2012, Queen Margaret University, Edinburgh, began offering a three-year business management honours degree.
Until recently, the four-year degree has been seen as the "gold standard" of Scottish higher education, but increasing pressure on public finances and growing student debt have seen the development of alternatives.
Abertay said the fast track degrees would be offered in business studies, computer arts, computer games application development, ethical hacking, food and consumer sciences, game design and production management and sports development with other programmes to be added in future if the pilot proves successful.
Professor Nigel Seaton, the university's principal, said: "The accelerated degree has exactly the same learning outcomes, quality standards and academic standing as the traditional four-year programmes.
"But by delivering it at a faster pace, we can offer our students more choice, creating alternative degree pathways we believe will suit the needs of some of our students."
Laurence Howells, chief executive of the Scottish Funding Council, which funds universities, said: "The new courses at Abertay University give students more choices about the way they study for a degree and the wide range of subjects they can choose is very exciting."
The fast-track option works by telescoping the last two years of a standard four-year programme into 15 months. All students will study at the same pace during their first two years, but will be offered the fast-track option at the beginning of their second year. If they choose to do so, then at the end of the second year they will move on to the accelerated programme.