Naismith, 25, has signed for the Toffees on a four-year deal after ending his contract with Rangers, who are soon to be liquidated and reformed as a new company following their financial crisis.
Although Rangers had hoped to transfer their existing playing staff onto the books of the new incarnation, Naismith refused, allowing him to join Everton as a free agent.
"It is a great honour to be joining a club of Everton's wonderful history and to have the chance to play with such a talented group of players in the world's best league in front of such a passionate group of fans," Naismith told the club's website.
"I look forward greatly to working with the manager David Moyes and all the staff at Everton and working hard to deliver on the pitch to repay their, and the chairman Mr [Bill] Kenwright's, faith and belief in me."
Moyes meanwhile said Naismith's versatility would represent a valuable addition to his squad. "We are delighted that Steven has agreed to join us," Moyes said.
"He will be an excellent addition to the players we already have and we look forward to him being fit and ready to play at the start of the season.
"He is an established international who can play in a number of positions. He has a flexibility we always like in our players and which will hopefully prove to be very useful for us."