Bardem, who won this year's Best Supporting Actor Oscar for No Country For Old Men, is thought to have proposed last month during a holiday in France.
Sources told the National Enquirer that he popped the question after mum Pilar urged him to take the relationship to the next level.
A friend said: "Pilar took her son aside and told him, 'What's the matter with you? She's perfect! You love her, she loves you. Get married.'"
The couple began dating last summer after hooking up on the set of Woody Allen's Vicky Cristina Barcelona in Spain.
The wedding is rumoured to be taking place later this year.