The Icelandic band's latest single 'Little Talks' climbs three places to number one on the chart, while Rita Ora falls to two with 'How We Do (Party)'.
Britain's Got Talent star Ryan O'Shaughnessy debuts at number three with 'No Name', Calvin Harris and Example are at four with 'We'll Be Coming Back' and Florence + the Machine are at five with 'Spectrum'.
Taylor Swift's new single 'We Are Never Ever Getting Back Together' lands at number 11, while Gym Class Heroes advance to 15 with 'The Fighter'.
Following Sunday night's London 2012 Olympic Closing Ceremony, Elbow are at 18 with 'One Day Like This', Emeli Sandé's at 19 with 'Read All About It, Pt III' and Kate Bush is at 22 with 'Running Up That Hill'.
Elsewhere, Cheryl Cole continues to climb with 'Under The Sun', which is up to 27, and George Michael's 'White Light' debuts at number 32.
This week's Irish Top 10 is as follows:
1. (4) Of Monsters and Men: 'Little Talks'
2. (1) Rita Ora: 'How We Do (Party)'
3. (-) Ryan O'Shaughnessy: 'No Name'
4. (2) Calvin Harris ft. Example: 'We'll Be Coming Back'
5. (3) Florence + the Machine: 'Spectrum (Say My Name)'
6. (7) Owl City and Carly Rae Jepsen: 'Good Time'
7. (5) will.i.am ft. Eva Simons: 'This Is Love'
8. (11) Wiley: 'Heatwave'
9. (10) fun.: 'Some Nights'
10. (6) Flo Rida: 'Whistle'
Watch the music video for Of Monsters and Men's 'Little Talks' below: