The 44-year-old will be in the dugout for Wednesday’s intimidating trip to champions Chelsea in the last 16 of the League Cup.
Unsworth is a firm favourite with the fans having served the club with distinction as a player, making 350 appearances during two spells at Goodison Park.
He gained kudos as a coach by guiding the Under-23 side to the Premier League 2 title last season.
“I’m a very proud man sat here preparing to lead Everton out tomorrow,” he told the media at his eve of match press conference.
“It doesn’t matter how many games I have, I’ll give it everything I’ve got.
“I spent the afternoon with the chairman yesterday and we spoke everything Everton.
“I’ll repeat myself from last time I sat here 18 months ago (he took charge of their final league game of the 2015/16 campaign after Roberto Martinez was fired), who wouldn’t want this job?
“The chairman has given me an opportunity to hopefully get a run of games where hopefully performance levels go up.
“From that, performances will dictate any future for me as Everton manager. I want to manage and this is an amazing club to be manager of. I make no secret of it.”
Koeman was sacked on Monday after a disastrous start to the season — despite the club spending £140 million ($185 million) on players in the summer — reached its nadir with a 5-2 spanking at home to Arsenal on Sunday leaving them mired in the bottom three.
Koeman for his part thanked the board for allowing him to take charge of a “great club”.
“I would like to place on record my thanks to the players and staff for all their work and commitment during my 16 months as Everton manager,” Koeman wrote on Twitter.
“Naturally I am disappointed at this moment but I wish the team good luck in the future.”
Unsworth — capped once by England — could be in charge for several matches leading up to the international break in a fortnight.
Everton have Premier League matches with Leicester City and in-form Watford to come with a trip to French side Lyon in the Europa League — the English side are bottom of their table — in between.
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