Tom marked the occasion with a hilarious photo posted to Instagram this morning (4 April), as they took a stroll around a shopping centre.
Guitarist Tom, who welcomed baby Buzz with wife Giovanna on 13 March, is seen posing with one hand and foot in the air, while having a firm grip on the pram handlebar.
Captioning the photo, the 'All About You' hitmaker said: "Our 1st proper outing."
Tom has been sharing plenty of snaps of himself and Buzz recently, while giving fans updates on his journey into fatherhood.
Earlier this week, Tom told fans that Buzz was having "tummy time" in a cute father and son bonding moment.
Meanwhile Giovanna, who is the sister of TOWIE star Mario Falcone, took to Twitter yesterday to update fans. She said: "Can't believe Buzz is 3 weeks old today! Wowser that's gone fast. Xx."
She also said this week: "Morning! My days seem to be lost in a world of Buzz cuddles, poop, wee, burps and feeding... It's a wonderful place to be. Xx."
Proud uncle Mario also told his Twitter followers this morning that he was off to see his baby nephew: "Today I am off to see my little nephew Buzz.. Can't wait for cuddles! And some sibling time with my sisters @MrsGiFletcher @giorginafalcone."
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Tom and Giovanna aren't alone! More stars who've welcomed babies in 2014 below:
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