It marks the band's fourth number one album in the UK following previous chart toppers Stadium Arcadium in 2006, Live In Hyde Park in 2004 and 2002's By The Way.
I'm With You is the band's first album to feature new guitarist Josh Klinghoffer, following the departure of John Frusciante in 2009.
Meanwhile, David Guetta has landed straight at number two with Nothing But The Beat, and Bombay Bicycle Club have scored their highest-charting album to date, with A Different Kind Of Fix reaching number six.
Lil Wayne's latest album Tha Carter IV, which is on course to break the iTunes record for single-week album sales, lands at number eight, while Dolly Parton goes straight in at number nine with Better Day.
Elsewhere on the chart, Beyoncé has achieved the highest-climbing record in the top 20, soaring to number 14 with her latest effort 4. It follows a surge in sales since her pregnancy announcement at the MTV VMAs.
The Top 10 in full:
1. (-) Red Hot Chili Peppers: 'I'm With You'
2. (-) David Guetta: 'Nothing But The Beat'
3. (1) Will Young - 'Echoes'
4. (3) Adele: '21'
5. (2) Joe McElderry: 'Classic'
6. (-) Bombay Bicycle Club: 'A Different Kind Of Fix'
7. (5) Adele: '19'
8. (-) Lil Wayne: 'Tha Carter IV'
9. (-) Dolly Parton: 'Better Day'
10. (6) Amy Winehouse: 'Back To Black'
Source: Official Charts Company
> This week's singles chart
Watch the video for 'The Adventures of Rain Dance Maggie', the lead single from Red Hot Chili Peppers's number one album I'm With You, below:
View the latest Official Top 100 Album Chart