Koeman is reunited with the Curacao international having brought him to England in 2015 whilst in charge of the south-coast club.
Martina did not feature in new Saints manager Mauricio Pellegrino's plans and was released at the end of his contract last month.
The 27-year-old, who made just nine Premier League appearances last season, joins the Toffees on a free transfer after putting pen to paper on a long-term deal until 2020.
"Everton is a big club with big ambitions and I'm really looking forward to joining this group of players and the manager as we try to step forward next season," Martina told his new club's official website.
"Obviously, I know the manager from my time at Southampton, so I know what he wants and he knows what I can do."
Koeman added: 'Cuco Martina is an experienced player who can perform in different positions at the back, which is important.
"It's also important, with the number of games we will face in the coming campaign, that we have strength and competition in the squad.
"I brought the player to Southampton, so I know what he can do for us here and this is why I've now brought him to Everton. He is a player who will strengthen our squad and be able to play in different positions when that's needed, too."