The Times-Mirror Co., which publishes the Los Angeles Times, Newsday, the Dallas Times-Herald and three other newpapers, yesterday agreed to purchase the Hartford (Conn.) Courant for $105.6 million.

The Courant, which began publishing in 1964 and bills itself as the nation's oldest continously published daily newspaper, is owned almost entirely by its employes, retired employes and their heirs. The sale is likely to make at least some of those employes millionaires.

The Courant has a daily morning circulation of 215,385 and a Sunday circulation of 288,186 according to audited figures for March 31, the most recent reporting period.

It has been the only major daily newspaper in Hartford since the afternoon Hartford Times ceased publication in October 1976.

The Courant is highly profitable, reporting net after-tax earnings of $3.7 million in 1978, on revenues of $53 .1 million, thus accounting for the high sale price in excess of $105 million. By comparison, the Washington Star, with a larger circulation, was sold 14 months ago for about $20 million.

Courant Vice President and Executive Editor Richard Mooney said the paper's board of directors had turned down an offer of "at least $70 million" from Capital Cities Communications Co., another chain, last November. He said that offer had "stirred interest in the Courant as a paper for sale," and resulted in the board learning that a majority of the employes were not opposed to selling the paper "for the right offer."

Courant President Edmund Downs, in a letter to the paper's 1,00 employes, said, "in the judgment of management, there is no newspaper company with which the Courant could be associated that has as much to offer the employes of the Courant and the community as does the Times-Mirror Co."

He said Times-Mirror had assured him that all management and operating personel would be retained, and that paper would maintain "local editorial independence."

Times-Mirror is no stranger to Connecticut. Two years ago it purchased two other Connecticut papers, The (Standard) Advocate and Greenwich Times.

The Times-Mirror offer involves both cash and installment credit and represents a value of $200 a share for each of the 527,770 shares of common stock outstanding.