The 'Moonrise Kingdom' actor tied the knot with Shauna Robertson - who he got engaged to in 2011 after six years of dating - some time in 2012, though no further information about the nuptials is available, Us Weekly magazine reports.
The news comes shortly after it emerged the couple became parents to a baby boy last month.
A source said: "Ed and Shauna are thrilled and excited for parenthood."
The 43-year-old actor and his film producer wife have not spoken out about the pregnancy and it was only confirmed in early March that Shauna was expecting.
However, friends revealed the actor was eagerly preparing for his first child, saying: "Ed is really excited for fatherhood. He helped pick out a stroller for the baby!"
Before dating Shauna, who has worked with Judd Apatow on movies including 'The 40-Year-Old Virgin' and 'Knocked Up', Edward dated Courtney Love and Salma Hayek.
He and Shauna co-founded fundraising site CrowdRise, which uses crowd-sourcing and incentives to encourage people to raise money for charity.
Edward recently started working on 'Birdman' with Emma Stone, Zach Galifianakis and his 'The Painted Veil' co-star Naomi Watts.