ESPN NFL Insider Adam Schefter reported the signing earlier in the day.
The signing allows Gronkowski, a tight end from Arizona, to join the team for the start of rookie camp.
The Patriots drafted Gronkowski with the 42nd pick. He had 75 receptions for 1,197 yards and 16 touchdowns in two seasons at Arizona.
The Patriots also confirmed the signing of second-round pick Jermaine Cunningham, which was reported by Schefter on Saturday, leaving inside linebacker Brandon Spikes (second round) and cornerback Devin McCourty (first round) as the lone remaining unsigned picks. A deal for Spikes is close, sources told ESPNBoston.com.
The Patriots grabbed Cunningham with the 53rd selection. He started 38 games at Florida and finished with 19½ sacks.
Information from The Associated Press contributed to this report.