Rhys was born in Cardiff, Wales, on 4 November 1974.His first language is Welsh.He grew up in Cardiff and attended Welsh-medium schools, Ysgol Gynradd Gymraeg Melin Gruffydd (in Whitchurch, Cardiff) and Ysgol Gyfun Gymraeg Glantaf (in Llandaff North, Cardiff). In 1993, he was awarded the Patricia Rothermere Scholarship.
At age 17, after playing Elvis Presley in a school musical, he applied to and was accepted at the Royal Academy of Dramatic Art (RADA) in London.
During Rhys's time at RADA, Rhys appeared in the BBC police series Backup as well as in House of America. He returned to Cardiff to act in his own language in the Welsh film Bydd yn Wrol (Be Brave),[ for which he won Best Actor at the BAFTA Cymru (Welsh BAFTAs).
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