"It's a boy!! Song of the day Beautiful Boy #johnlennon," wrote Wood on Monday.
Bell tweeted: "Wow! What a day. Evan you are my warrior! You never cease to amaze. Thank you for birthing our son so naturally and peacefully. You did it!"
Later on Wood replied saying: "And you are mine. Thank you for being there and helping me through it. I love you both more than words can say."
Bell, 27, announced that they were expecting their first child in January.
He married the 25-year-old actress in California last year.
Bell rose to fame in the British film Billy Elliot in 2000, where he played a talented young ballet dancer. The film was later turned into a stage show.
Since then he has starred in Peter Jackson's King Kong remake and provided the voice of Tintin in Steven Spielberg's The Adventures of Tintin: The Secret Of The Unicorn.
He is confirmed for the next Tintin movie and will also appear in Snowpiercer, along with Octavia Spencer, Chris Evans and Tilda Swinton, later this year.
Wood has starred in the hit US vampire drama True Blood, as well as the TV miniseries Mildred Pierce alongside Kate Winslet.
She is also known for film roles in The Wrestler and Thirteen.
The pair first dated in 2005 but split up after a year before later getting back together.
