On 10th of March, 2004, Anthony became father with his ex fiancée, Lucy Bolster. He was engaged with Lucy Bolster somewhere in 2003 and they also promised to get married soon and be each other’s loving spouse but it didn't happen at the end. They called off their engagement.
In December 2013, Anthony got engaged with Rosanna Jasmin. He also revealed that they were in love affairs since one and half year. The same time he also announced that they were also expecting their first child together and they finally welcomed it in June of 2014.
Anthony's first ever acting role was in the television sitcom, Chalk. After that he was seen in the television series Grange Hill. In 2000, he became associated with his fellow mates Duncan James, Lee Ryan and Simon Webbe and formed their own musical band, Blue. On 26th of November 2001, they released their first album All Rise. He is also the solo singer and has released his debut solo single in 2006 under the title Do You Ever Think of Me. Costa's salary and net worth is said to be high.