The shift is due to take place in April next year, and, provided no other publications get there before then, should make the the first major national newspaper in the US to abandon print.
A "modest reduction" in editorial staff is expected when the daily print edition ceases publishing.
The Christian Science Monitor was set up by Mary Baker Eddy, after the Christian Science religion she founded had been criticised in the press. It has a motto that its writing should "injure no man, but bless all mankind".
In spite of its name, the respected title is not a Christian newspaper, and its journalists have collectively won seven Pulitzer Prizes.
Christian Science Publishing, the owner of the Monitor, argues that the switch to web-only journalism is in keeping with Eddy's edict that the paper must "keep abreast of the times" and that the cost savings will help it maintain its journalistic standards.
John Yemma, editor of the paper, said: "In the Monitor's next century, as with its first century, it is committed to finding answers to the world's most important problems, asking the questions that matter and getting the story behind the news - all of which is staying true to Mrs. Eddy's unselfish, original vision.
"The Monitor's role is right there in its name. It's to monitor the world, to keep an eye on the world from a perspective of hope."
Yemma added that there would be "a modest reduction" among the paper's 95 editorial staff, which was likely after the move to online was completed.
The paper had a circulation as high as 220,000 in the 1970s, but now sells around 52,000 copies each day, while the website attracts 1.5m visitors a month.
It is forecast to lose $18.9m in the year ending April 30. The switch to web-only publication is projected to help cut this loss to $10.5m by 2013.
It is a development that will be watched closely by other newspaper publishers already struggling to maintain circulation levels and now facing the added threat of a significant fall in advertising revenue in 2009.
However, because the Monitor is run as a non-profit business, and is subsidised, its experience is somewhat different to most newspapers.
The end of the Christian Science Monitor as a daily newspaper comes at a tough time for the US newpaper industry as hundreds lose their jobs across the country.
Yesterday, Tribune Co's Los Angeles Times announced it was to cut 10% of its editorial staff, laying-off 75 employees as part of a 200-person reduction that began last week.
The New York Times cut jobs earlier this year and USA Today's owner, Gannett, is also cutting more jobs having announced 120 were to go in August.
The Star-Ledger, the biggest newspaper in New Jersey, said last week it was to make about 40% of its newsroom staff redundant with around 150 jobs going.
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