Idris was born in Peckham, south-east London, and is of Nigerian descent. He is the youngest of six children raised by a single mother. He played football and dreamed of being the next Cristiano Ronaldo. He also played rugby, and in 2002 he shook the hand of Queen Elizabeth II when his team took part in her Golden Jubilee. Idris's elder siblings—three brothers and two sisters—have all gone on to corporate careers in law, Business, and IT, so when he realised a professional football career wasn't going to happen, he ended up studying drama at Brunel University London. He received a BA Honours degree in Theatre, Film & Television studies.

At Brunel, Idris met Actress Cathy Tyson, who encouraged him to meet Ade Solanke and audition for a part in her play, Pandora's Box. He got the role, signed with an agent and began performing in more plays. He also trained at the Identity School of Acting, founded by Femi Oguns. After performing at the Royal National Theatre in London, Idris decided to pursue television and film roles. He had several parts on British series including Miranda (2013), Doctors (2015) and Casualty (2015).

Idris had his first big screen part in 2016 in the British thriller City of Tiny Lights, starring Riz Ahmed. In 2017, he made his American film debut in Megan Leavey alongside Kate Mara, who plays the title character in the eponymous war film. Idris also has a part in the 2018 film The Commuter with Liam Neeson; and has been cast in Farming, alongside Kate Beckinsale. Farming is a semi-autobiographical story of Nigerian-British actor Adewale Akinnuoye-Agbaje, who will direct. Idris will play the character based on Akinnuoye-Agbaje, who, like many Nigerian children in the late 20th century, was "farmed out" to a white family in the UK in the hopes of a better life, while Beckinsale will portray his strict foster mother.

Idris is a devoted football fan and supports Manchester United. He said his hero is American actor Denzel Washington. In 2017, he told Interview magazine, "[Denzel is] phenomenal. I didn't know I wanted to be an actor, but once it found me I looked at whom people were saying were great. I looked at who I wanted to be like. Not just in acting, but in their personal life as well. Being a well-rounded person, a fine Example of good taste and prestige and class, that's what I really chased, so he was the person that did it for me."