Assuming they pass, they are expected to head to Clearwater, Fla., to begin their careers with the Gulf Coast League Phillies.
It is unclear how much Moniak's signing bonus will be, but it will be less than the $9,015,000 allotted for the No. 1 pick. Gowdy, a second-round pick, will sign for more than the allotted $1,536,200 for the 42nd overall pick.
Moniak and Gowdy had both committed to UCLA. Stobbe, a third-round pick, had committed to Arkansas.
The Phillies already have agreed to a $312,700 deal with sixth-round pick David Martinelli, who is an outfielder from Dallas Baptist University. Other notable agreements include: Ole Miss catcher Henri Lartigue (seventh round), UCLA right-hander Grant Dyer (eighth round), Cal State Fullerton right-hander Blake Quinn (ninth round), Metro State University right-hander Julian Garcia (10th round), Central Union High School right-hander Justin Miller (12th round), Cal Poly San Luis Obispo catcher Brett Barbier (16th round) and Indiana right-hander Jake Kelzer (18th round).
Todd Zolecki has covered the Phillies since 2003, and for MLB.com since 2009. Read his Phillies blog The Zo Zone, follow him on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.