According the this wiki article Pettigrew went into hiding when Death Eaters suspected him of being a traitor (After the fall of What’s-His-Face). He chose a wizarding family so he could keep track of the wizarding news and to rejoin his master should he return to power.

The wizarding family Pettigrew chose happened to be the Weasley family. Sounds like he imposed himself upon them (as a rat) until he was discovered,

He lived with the Weasley family, who named him Scabbers. He was Percy’s pet rat, than Ron’s, when Ron went to Hogwarts.

I think it was almost immediately after Harry’s parents were killed, as @SABOTEUR described.