The 21-year-old made a £37m switch from Schalke 04 to the Etihad Stadium last summer for his first taste of football outside of his native Germany.
Guardiola pinpoints the 2-1 win over Arsenal shortly before Christmas as the moment Sane truly arrived at City, having scored three and registered three assists in his six outings since then - including a key role in Raheem Sterling's opener against Bournemouth on Monday.
"The people say in the winter transfer window one guy arrived - Gabriel Jesus," the former Barcelona boss told reporters. "I think two arrived. Leroy arrived a little bit scared. But, since the game against Arsenal, I think he made a click.
"He showed us a lot of things. He is so fast, his intensity helps us a lot and he helps us defensively, too. And he's only 21 years old. I'm so happy for Manchester City, who will have a good player for the next few years."
Sane has averaged more successful dribbles for City this season than any other player, while also ranking highly for ball recoveries and tackles won.