The duo are now committed to Goodison Park until the end of the 2014-15 season.
The news gives Everton a lift following the loss of influential midfielder Steven Pienaar to Tottenham earlier this week.
Rapid rise: Irishman Coleman has earned a new contract after impressing Goodison Park manager Moyes
Irish winger or full-back Coleman, 22, signed his previous contract only last season but has been rewarded for his outstanding form during the current campaign.
Coleman joined the Toffees from Sligo Rovers for £60,000 in 2009 and, after a loan spell at Blackpool last year, has now established himself as a regular in the first team.
He has been one of David Moyes' most reliable players this term and has scored five times.
Academy product Anichebe, also 22, would have been out of contract in the summer. The Nigeria forward has been hampered by injuries over the past two seasons and had been linked with a move away from the club.
The way forward: Striker Anichebe, who has been with Everton since 2005, has pledged his future to the club
However, Moyes has acted quickly to tie him to a new deal following Pienaar's departure.
With Yakubu having also joined Leicester on loan, Moyes, who has little funds to recruit, can ill afford to lose many more players.
Moyes has said he must concentrate on the loan market in order to bring players in this month, but it remains to be seen if fees received for Pienaar and Yakubu allow him more flexibility.
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