It made the announcement as it reported a fall in profits and underlying sales over the past 12 months.
Morrisons is the UK's fourth largest supermarket, but unlike its rivals does not have an online retail presence.
Chief executive Dalton Philips called the move "an important step". A deal on technology with online food retailer Ocado is one option being discussed.
"We will be transacting online with food by the end of this year," he told the BBC's Today programme. "We've been studying the market for two years [and] it's a market that is accelerating very quickly."
A possible deal with Ocado was "one of the options available", he added.
Morrisons reported a 7.2% fall in pre-tax profits to Â£879m for the year to 3 February - its first fall in full-year profits for six years.
Like-for-like sales were down more than 2%.
Other supermarkets have seen sales growth in their online businesses and in smaller convenience stores.
Rivals Tesco, Sainsbury's and Asda, the other members of UK's "big four" supermarkets, have been operating online shops for a number of years, and online food shopping is growing by about 20% a year.
Morrisons also said it would open 100 convenience stores in the coming months, adding to 12 "M Local" stores it had already opened.
The convenience stores market, which includes Sainsbury's Local and Tesco Express stores, is seeing annual growth of 6%.
The changes come at the end of what Morrisons described as "a difficult year".
"The sustained pressure on consumer spending was reflected in our like-for-like sales performance, which was not as good as it should have been," Mr Philips said.
"We have implemented a range of measures to address this. Today's announcement that we are launching an online food offer... is another important step."
Investors responded positively. Shares in Morrisons rose by more than 3.5% in early trading.
Ocado saw its shares jump 24.5% in the first hour of trading, after it reported a strong rise in sales over the Christmas and New Year period, on top of news about a possible technology-licensing agreement with Morrisons.
It said gross sales for the 12 weeks to the end of February were up 14.4% compared with the same period a year ago.
Supermarket chain Morrisons says it will begin selling food online by the end of this year.