When does a bill officially become a law?

A bill becomes law if signed by the President or if not within 10 days and Congress is in session. If Congress adjourns before the 10 days and the President has not signed the bill then it does not become law

If the governor neither vetoes nor signs the bill within 10 days, the bill becomes a law. If a bill is sent to the governor within 10 days of final adjournment, the governor has until 20 days after final adjournment to sign the bill, veto it, or allow it to become law without a signature.