Terry believes the 32-year-old former Cameroon striker - a prolific scorer at Mallorca, Barcelona, Inter Milan and Anzhi Makhachkala - remains a deadly finisher.
"I said to him (Eto'o) 'thank God you're here' because I've had so many battles against him," Terry told Chelsea TV.
"He's such a threat, he's obviously a few years older but he still looks very sharp and hungry.
"He's got an eye for goal and I think he'll be a good addition, he was welcomed straight into the squad."
Terry suspects that Eto'o and Willian, who also left Anzhi for Stamford Bridge at the end of the transfer window, may need more time to adjust from the Russian league.
"Eto's looked really sharp in training so far, and so has Willian," the England defender said.
"You speak to them and they talk about how the intensity of their training (in Russia) is a lot different to how it is here.
"So for sure it will take them a few weeks to get their full fitness, but once they do they'll both look very good."
While Terry approves of Eto'o's arrival, the African's former Anzhi team-mate Roberto Carlos has sounded a note of caution over his potential to disrupt the squad.
"I've known Eto'o since he was 16. He's a good person and I've always liked him, but he always thinks of himself, not the group," Brazilian great Carlos told Globoesporte.
"It's quite confusing and odd when a footballer, instead of playing, is interested in bringing in players who are his friends. He did everything at Anzhi, except play football.
"There were a few small problems in the dressing room with the arrival of Eto'o, which were resolved. His signing had to be explained to several players.
"Then there came a point when Samuel wanted to interfere in my work. He wanted to control the club, taking my place and that of the coach, Guus Hiddink."