Smith said that Jones, a 17-year-old third base prospect from the Dominican Republic, has cleared the final round of paperwork from the Major League Baseball offices.
Jones agreed to a contract with the Padres worth $900,000.
"For me, we got a premium prospect for a 30 percent discount," Smith said.
In December, Jones agreed to a $1.3 million contract with the San Francisco Giants. One month later, Jones' contract was voided after he failed a team-administered drug test that was part of his physical.
After the Giants voided the contract, Major League Baseball conducted an investigation that determined Jones had violated baseball's Minor League drug policy. That means he has to serve a 50-game suspension.
Smith said that suspension will start on Saturday, when the Dominican Summer League starts. Smith hopes Jones will be back playing again in late July.
Jones recently passed his physical with the Padres that included testing for performance-enhancing drugs. Earlier this week, he received clearance from Major League Baseball that verified his identity and age, standard procedures, Smith said.
Smith feels the Padres did their due diligence on Jones.
"I think you look at the kid, the makeup and realize sometimes these kids have no idea what they're doing because of the advice they're getting," Smith said. "At 16 years old, guys make mistakes. You have to get in and investigate the player and family.
"We felt comfortable going forward."
When Jones' contract was voided by the Giants, Smith dispatched Felix Feliz, who is the Padres coordinator of Latin American scouting, to contact Jones.
"I had seen him several times before he signed initially. I talked to Felix and I told him, 'Let's get on this guy.' We got back on him and stayed on him. We had come over to our [Dominican] complex a few times. We were finally able to come to terms."
What does Smith like about Jones?
"He's 6-foot-3, 195 pounds and has a great build, broad shoulders, he almost looks like a young [Adrian] Beltre at third base," Smith said. "He has good bat speed with plus-power potential, a plus arm and good agility for his size. I like the makeup, too. He's one of the premium offensive guys over there.
"He's pretty advanced as far as his approach."
Corey Brock is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.