The 27-year-old has signed a three-year contract with the Toffees following the expiration of his deal with the Saints.
It was now-Everton boss Ronald Koeman that brought Martina to Southampton from FC Twente in 2015, and the Curaco captain has revealed that he is looking forward to linking up with the Dutchman once again.
"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 the 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. Everton supporters are really passionate about their club and everyone's excited about where the club is aiming. You can see this is a club that wants to achieve something and the players we are bringing certainly show this.
"When you come to a new club, you need to get to know one another so the training camp in Holland will be great for me and for the other new players as well. We will play against Twente, one of my old clubs too, and I'm really looking forward to showing everyone 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."
Martina, 27, started just six Premier League matches for Southampton last season, although he did appear five times in the Europa League.