In a statement, the university says that all “outstanding issues between the two parties have been resolved”.
Professor King was suspended in February by the university court “pending investigation of a number of issues”.
Earlier this month, the university claimed that Professor King had retired, prompting him to issue a denial and accuse Abertay of acting in an “unfair and unlawful” manner.
A spokesman for Professor King said at the time that “his position is that he has not retired and he remains in dispute with the university over the terms of an extension of contract agreed with the university last year”.
He also said that an employment tribunal would take place later in the year over “the principal's claims of age discrimination and whistle-blowing”.
The statement released today, which the university said was made jointly with Professor King, says that he made a “unique contribution to its development and success over his 19 years stewardship”.
It says the university court has renamed the library the Bernard King library “as a tribute to Professor King's achievements”.
The university said it would not comment any further on why legal claims had been withdrawn and on what terms.
A spokeswoman said the university would not comment on a “legal matter between the university and the principal”.
Professor King’s spokesman said he was forbidden from commenting separately by the terms of his agreement with Abertay.
During the dispute over Professor King’s suspension, the university lost five members of its court and one pro vice-chancellor.
Through a series of leaked letters, it emerged that there had been a dispute between the university court and senior academics last November over when Professor King should retire.
It is understood that the agreement between Professor King and the university involved a financial settlement.