The post comes after Brooklyn accused his parents, David and Victoria Beckham, of "trying endlessly to ruin my relationship since before my wedding, and it hasn't stopped", in a social media post in January.
He also alleged his wife had been disrespected by his family.
"Happy Valentine's Day baby, I am the luckiest person in the world to be able to call you my Valentine's every year," Brooklyn Pelz Beckham's Instagram post read.
"I love you more than you know and I will forever protect and love you."
The post was accompanied by a black-and-white picture of the pair kissing, with Brooklyn shirtless and Nicola in a crop top.
Brooklyn's January social posts said he does not want to reconcile with his family, having accused former England footballer David Beckham and ex-Spice Girls singer Victoria Beckham of prioritising "Brand Beckham" over all else and controlling narratives in the press.
DJ Fat Tony, who performed at the wedding, said on UK broadcaster ITV in January the feud began when American singer Marc Anthony had asked for "the most beautiful woman in the room" to come to the stage at the wedding.
Guests were said to have believed it was for Nicola's first dance with Brooklyn, but instead Victoria Beckham was called to the stage and asked to dance with her son, prompting Nicola to leave the room in tears.
"What it was, was - and why I said it was inappropriate as well - was because it was the timing. What happened was, basically, Marc Anthony was performing on stage, he then called Brooklyn onto the stage," DJ Fat Tony said.
"Brooklyn went onto the stage, and the next minute everyone's expecting it to be Nicola to go up and do the first dance, and then Marc asked for the most beautiful woman in the room to come to the stage - and then he says, 'Victoria, come to the stage'.
"So Victoria is by the stage, she goes onto the stage, and of course, at that point, Brooklyn is literally devastated because he thought he was going to do his first dance with his wife, then Nicola leaves the room crying her eyes out.
"Brooklyn is stuck there on stage, and they do this dance, and Marc Anthony says 'put your hands on your mother's hips' and it was a Latin thing, and the whole situation was really awkward for everyone in the room."
However, Anthony told US outlet The Hollywood Reporter that how the feud had come out is "hardly the truth".
David and Victoria Beckham have been contacted for comment.
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