Anzhi did not disclose the fee but media reports said it was around 30 million euros, adding the four-times African Footballer of the Year could become the richest player in the world on an annual salary of 20 million euros.
"The transfer sum has been agreed," said the wealthy team from the volatile North Caucasus region who are bankrolled by Russian billionaire Suleiman Kerimov.
"The player will undergo a medical and if he passes it he will sign a three-year contract," the club said on their website.
Eto'o, 30, won two Champions League titles with Barcelona before joining Inter in 2009. He won a Serie A, Italian Cup and Champions League treble in his first season in Italy.
Anzhi, who also boast Brazilian left-back Roberto Carlos and former Chelsea midfielder Yuri Zhirkov, said Eto'o could make his league debut this weekend.
"Samuel should arrive on Thursday to begin preparation for our league match at Rostov," said Anzhi who play their home games in Makhachkala but train near Moscow.
Anzhi general director German Chistyakov dismissed media reports Eto'o would live in Milan and only travel to Makhachkala for home matches.
"This is nonsense," Chistyakov told Reuters. "Samuel will live in Moscow after he selects a place for himself and his family."
He added Eto'o would be presented to the fans before Anzhi's next home match against Volga Nizhny Novgorod on September 11.
