Soller was educated at the Royal Academy of Dramatic Arts in London.
Soller's breakthrough role was in The Glass Menagerie at The Young Vic. He acted in many plays in his early career including The Talented Mr Ripley and Edward II at the National Theatre for which he was nominated for Best Supporting Actor.
Soller's notable films include Anna Karenina in 2013. He had a supporting role in the TV show An Inspector Calls and played Clifford in The Hollow Crown: The Wars of Roses.
Soller is married to English actress Phoebe Fox.