The comedian will play the opening night at the London-based festival on July 7, while Faith will headline the closing concert on July 17.
Katy B has been confirmed for July 8, The Temper Trap will play on July 11 and Anna Calvi will perform a set on July 12.
Jill Scott, The Enemy, Tindersticks and M83 will also play sets throughout July at Somerset House.
Tickets go on general sale from April 27 at 9am and are priced between £22.50 and £35 (plus booking fee).
The full lineup for Somerset House's Summer Series 2012 is as follows:
July 7 - Tim Minchin
July 8 - Katy B
July 9 - Jill Scott
July 10 - Jill Scott
July 11 - The Temper Trap
July 12 - Anna Calvi
July 13 - The Enemy
July 14 - DJ Abrantee Presents Afrobeats Night featuring Olu Maintain, Cappo Snoop, Atumpan, Scene May7en and Vibe Squad
July 15 - Tindersticks
July 16 - M83
July 17 - Paloma Faith
> Paloma Faith reveals new album 'Fall To Grace' artwork
Watch the music video for Paloma Faith's 'Picking Up The Pieces' below: