Eastwood started his career as a youth player with Huddersfield Town. He went professional in 2007, but struggled to break into the first team and was loaned to Woking in 2008 and Bradford City in 2009. He made a permanent transfer to Oxford United in 2010 but did not make a first-team appearance, and in the following years he played for FC Halifax Town, Portsmouth, and Blackburn Rovers. Eastwood has played internationally for England twice at under-18 and under-19 levels. In June 2016, Eastwood returned to Oxford United on a 1 year contract. He was given the number 1 jersey and played every minute of all first-team matches in 2016–17, including the EFL Trophy Final at Wembley Stadium. He signed a two-year contract extension in February 2017, and was voted the Supporters' and Players' Player of the Year at the club's end-of-season awards.