Koeman was Everton’s first choice following the dismissal of Martinez ahead of the final game of last season.
The likes of Frank de Boer, David Moyes, Unai Emery and Manuel Pellegrini were considered, but Kenwright believes Koeman will lead the club forward.
“We are really pleased to have secured the man who was our No 1 target from the moment we set out to appoint a new manager,” said Kenwright.
“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.”