Gabriel was linked with a number of clubs including Manchester United and Napoli but Arsenal have agreed a €30 million (£27m) deal with Lille.
According to Fabrizio Romano, Gabriel has now completed his medical with Arsenal and has put pen to paper on a five-year deal.
Arsenal will officially announce their new signing before the end of the week.
Gabriel is expected to form a new-look partnership alongside William Saliba at the heart of Arsenal’s defence.
“I feel he is among the top five dominant central defenders in Europe right now,’ Lille president Gerard Lopez said of Gabriel.
“His statistics, which aren’t well covered outside of France, show that his percentage for winning duels is pretty unheard of in a league that’s extremely physical.
“He’s an absolute machine, so to me, he’s well on his way – if not this year – to potentially a really big club.
“I’m certain he’s on his way to the Brazilian national team at some point.”