The Official Charts Company announced her record after What’s My Name? rose from number two to the top spot.
The last solo artist to achieve the feat was Elvis Presley, who had number ones in each year from 1957 to 1963.
Rihanna’s album Loud also holds on to its number one slot, giving her the second UK chart double of her career.
In 2007, her album Good Girl Gone Bad and single Umbrella topped both charts simultaneously.
Loud has now sold nearly 900,000 copies since its release in November last year.
As well as her number one, Rihanna, who is 22 and from Barbados, also appears on two other songs in the top 10 – Only Girl (In The World) and Who’s That Chick.
Only Girl (In The World) was a number one last year and followed other number ones for Run This Town (2009), Take A Bow (2008) and Umbrella (2007).
Other albums which have re-entered the top 10 are Plan B’s The Defamation of Strickland Banks, Rumer’s Seasons Of My Soul and Cee Lo Green’s The Lady Killer which climbs to its highest chart position yet at number four.
In the singles chart, the BBC’s Sound Of 2011 winner, Jessie J, climbs to number five from last week’s 18 with Do It Like A Dude. – Bbc