Recordings released on paid-subscription platforms such as Spotify, Apple Music and Tidal will now qualify.
Nominees previously had to be available on a CD, or downloadable.
Grammy members will also vote in fewer categories, the Recording Academy announced.
The changes will come into force in time for next February's awards.
Bill Freimuth, the Academy's senior vice president of awards, said: "We noticed that there were a number of higher-profile artists who were choosing - for philosophical reasons as much as anything - to release their music through streaming-only, and we did not want to be exclusionary toward them."
Some musicians, including Prince and Beyonce, have released debuts exclusively on Tidal, before then releasing them on iTunes and other platforms.
Grammy members will also have the number of categories they can vote in reduced from 20 to 15. However all members will still be able to vote in the top four categories: album of the year, song of the year, record of the year and best new artist.
Other changes include an update for the best new artist category. Rules now allow a performer who releases at least five singles to qualify. Previously, acts had to release an album to be eligible. Acts can qualify for best new artist until they have released three albums or 30 singles.
The best rap/sung collaboration, which was given to rap and R&B acts who team up on a track, is being renamed to best rap/sung performance, and can now be given to solo acts.
Best blues album has also been split into two categories: best traditional blues album and best contemporary blues album.
Freimuth added: "The effort here is to protect the integrity of the Grammy Awards, and so sometimes that means typing up some rules, and sometimes that means loosening up some rules, sometimes that means contracting a category, sometimes that means adding a category."
This year's awards saw Taylor Swift's 1989 win the coveted album of the year award.
The singer - who is the first woman to win the award twice - also won best pop vocal album and best music video, for her track Bad Blood.
Rapper Kendrick Lamar won the most prizes on the night with five awards.
British singer Ed Sheeran also won his first two Grammys for song of the year and best pop solo performance, for his number one hit Thinking Out Loud.
Songs need to have been released between 1 October 2015 and 30 September 2016 to be eligible for next year's awards. The nominations will be announced on 6 December.
Songs released only on streaming services are to be eligible for Grammy nominations for the first time, as part of changes to the music awards' rules.