Before Hodgson's appointment was confirmed he was interviewed by Sky Sports at the club's training ground.
He has watched from afar as the south Londoners lost three more games to end Frank de Boer's short reign at the club.
De Boer sacked after only four games
He has been out of management since quitting England after their last-16 defeat by Iceland at Euro 2016.
Palace dismissed De Boer after they suffered the worst start to an English top-flight campaign for almost 100 years - failing to win or even score a goal.
"In those days I had dreams of playing for the team, then as a coach you think about coaching the team and a lot has happened in between times".
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"It's a good day for me, I'm very happy and looking forward to hopefully getting down to work and trying to help us get some points in the league and climb up the table".
"It is very rewarding to find myself here now, in different times, as the Palace manager at a club that I have always loved and admired with a huge potential", he added.
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Crystal Palace are now rooted to the bottom of the Premier League table having lost all four of their opening games.
A well-travelled and globally respected coach who has worked at clubs in England, Sweden, Switzerland, Italy, Denmark and Norway, Hodgson will extend his managerial career to a 41st year.
Hodgson is the club's seventh permanent manager in the past six years.
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Hodgson's last job was as manager of England. The appointment of a first team coach is also expected imminently.
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