The couple tied the knot at Paltrow's home in New York on 29 September in front of a host of celebrity guests, including Robert Downey Jr, Steven Spielberg and Cameron Diaz.
Paltrow posted a picture from the big day showing the newlyweds walking down the aisle, with the words "for those who have requested, a little look inside the best day of our lives. #thefaltrows".
The 46-year-old US actress wore a custom lace Valentino Couture gown for the occasion while the men donned Tom Ford suits.
Friends and family threw flower petals in the direction of the couple while Apple Martin, Paltrow's 14-year-old daughter with former partner Chris Martin, can be seen in the background.
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Paltrow announced her engagement to 47-year-old Falchuk in January after dating him for three years.