Nicholls signed a scholarship with Wigan Athletic in 2009. In 2010, he was named in the England U19 squad that reached the semi-finals of the UEFA European Under-19 Championships, but did not make an appearance in the tournament. He made his debut for the team in February 2011 in a 1–0 defeat against Germany. After a series of impressive performances for the Wigan Athletic reserve team, he appeared for the first-team as a substitute for the first time on 2 January 2010 in a 4–1 FA Cup third round victory over Hull City. Later that month, he signed a two and a half-year professional contract with the club, which he then extended in January 2012. In between loan spells, Nicholls made his league debut on October 27th 2013 in a goalless draw away to Charlton Athletic. Following the expiry of his contract with Wigan in August 2016, Nicholls joined MK Dons, signing a two-year deal. In his first season for the club, Nicholls' made a total of sixteen appearances in all competitions, achieving two clean sheets. In May 2021, Nicholls signed for Huddersfield Town on a two-year deal and went on to have a successful debut season, achieving 19 clean sheets and playing a huge role in them reaching the 2022 Championship play-off Final. He was later named in both the EFL Championship Team of the Season and Professional Footballers' Association Team of the Year.