Monaghan was born in Berlin, Germany, to British parents: Maureen, a nurse, and Austin Monaghan, a science teacher. Monaghan has a brother, Matthew, who is a year older, and is a teacher, singer and musician. Monaghan's family lived in Berlin, Düsseldorf, Stuttgart, and Münster, moving about every four years.
When he was about 11 years old, his family moved from Germany to Heaton Moor in Stockport, Greater Manchester, and later to Manchester. Monaghan's first language is English, but he also speaks some German and is well known for his ability to impersonate others and replicate accents.