Bill Kenwright has spoken following the Dutchman's Goodison Park appointment.
Kenwright is onto manager number 4 at Everton
Martinez was relieved of his duties in May, following consecutive bottom-half finishes in the Premier League.
A string of big name bosses - including Mark Hughes, Frank de Boer, David Moyes and Unai Emery - were all linked to the post alongside Koeman, whose three-year deal was finally confirmed on Tuesday following a lengthy pursuit, after Southampton reluctantly accepted his resignation.
Moyes was linked with a Toffees return
And Kenwright told Evertonfc.com: "We are really pleased to have secured the man who was our number 1 target from the moment we set out to appoint a new manager.
"Ronald has such a strong track record in the game, instantly commanding respect for what he achieved as a player and for his qualities and accomplishments as a manager.
"The hopes and aspirations that we all have as Evertonians are with him, as is our total support at Board, shareholder and fan level."
Remarkably, Koeman is only the fourth permanent manager in Kenwright's 16 and a half years as Everton chairman.
The 53-year-old - a three-time league winner in the Netherlands and a domestic cup winner in both his homeland and Spain - led Southampton to record Premier League finishes in both his seasons in charge.
Sevilla's Emery was another who was heavily linked
Such credentials were tough for the Toffees to ignore, clearly, despite the recent success of Emery in Seville.
The Spaniard, who has won three straight Europa Leagues with the Andalusians, is expected to take over at Paris Saint-Germain instead.
It is unclear if Everton have retained an interest in Sevilla sporting director Monchi.