Renck was born on 5 December 1966 in Uppsala, Sweden.

Stakka Bo scored a hit single in 1993/1994 with the song "Here We Go", which peaked at #13 in the UK Singles Chart. The song appeared in an episode of the animated television series Beavis and Butt-Head, in the films Prêt-à-porter, Never Been Kissed, Alien Autopsy and in the video game UEFA Euro 2004.

Renck directed three episodes of AMC television drama Breaking Bad, one episode of The Walking Dead and one episode of Halt and Catch Fire. Renck's first film, Downloading Nancy, 2008 premiered at the Sundance Film Festival on 21 January 2008 in Park City, Utah. In addition, Renck directed a fashion art film called Decadent Control for Imagine Fashion, which premiered in March 2011. It starred Roberto Cavalli, Eva Herzigová, Kirsty Hume and Brad Kroenig and used fashion from Agent Provocateur and H&M.

He has directed music videos for a number of artists including Madonna's "Nothing Really Matters" and "Hung Up", Kylie Minogue's "Love at First Sight", All Saints' "Black Coffee", Robyn's "Handle Me", Robbie Williams's "Tripping" and "She's Madonna", The Libertines' "What Became of the Likely Lads", Suede's "She's in Fashion", New Order's "Crystal" and "Krafty", Beyoncé's "Me, Myself and I", Chris Cornell's "Can't Change Me", The Knife's "Pass This On", Fever Ray's "Seven" and Bat for Lashes' "Daniel". In 2012 he directed the music video "Blue Velvet" for Lana Del Rey which was also used for the commercial campaign by H&M, as well as the music video for "Wild" by Beach House. In 2015 he directed the ten-minute video for David Bowie's "Blackstar", as well as the video for Bowie's "Lazarus" that appeared in January 2016. In 2005, he and his brother Martin directed two videos from Swedish band The Cardigans: "I Need Some Fine Wine and You, You Need to Be Nicer" and "Don't Blame Your Daughter (Diamonds)".