Mr Murphy also said that he would plug any funding gap faced by Scottish institutions as a result of a reduction in tuition fees for English students from £9,000 to £6,000 by a Labour administration at Westminster.
The MP was due to outline his higher education policy on a visit to Glasgow Caledonian University on 3 March.
“Under Scottish Labour there will be no university tuition fees in Scotland,” Mr Murphy said beforehand. “I want young Scots to be able to train to be doctors, teachers, lawyers, engineers, scientists and much more, no matter their background or how much money their parents have.”
Tuition fees were abolished by Scottish Labour’s then-first minister Donald Dewar in 2000, but students still paid an endowment of about £2,000 on graduation until this was abolished by the Scottish National Party in 2008.
Mr Murphy’s position contrasts with that of his predecessor as Scottish Labour leader, Johann Lamont, who said in 2012 that it was “not viable” to fund a mass participation higher education sector using only public funds and claimed that such a system was “essentially regressive” because it helped a disproportionate number of graduates from privileged backgrounds.
Scottish universities have raised concerns that they would face a multimillion-pound funding gap if Labour reduced tuition fees in England, since the Holyrood parliament has passed legislation stating that no student from the rest of the UK would be charged more to study in Scotland than they would elsewhere in the country.
Since public funding would be used to compensate English universities for any reduction in fees, Scotland could expect a significant payment under the Barnett formula. However, the SNP government is yet to say whether it would direct any additional funding towards universities.
Mr Murphy said that he would “use the extra money coming to Scotland to plug any immediate funding gaps as a result of any fees reduction in England”.
His comments were welcomed by Gordon Maloney, the president of NUS Scotland.
“Today’s welcome announcement marks a broad consensus against fees for Scottish students, and against charging in Scottish higher education, which should settle the debate once and for all,” he said.
But Mr Murphy was accused of “shameless hypocrisy” by SNP MSP Stewart Maxwell, who highlighted how the Labour MP had voted in favour of the introduction of tuition fees in 1998.
“[The] announcement today is all about panicked attempts to grab headlines – and nothing to do with defending the principle of free education,” Mr Maxwell said. “With [Labour’s] appalling track record on fees, it’s clear that students in Scotland won’t be fooled by this shameless stunt.”