Rizzo, 23, is the second young Cubs player to receive a long-term extension. Shortstop Starlin Castro was rewarded with a seven-year, $60 million contract last August.
"Now, you don't have pressure," Castro said. "You have your contract, your family is good. The only thing you have to put in your mind is play hard and help your team win."
With the two signings, general manager Jed Hoyer sent a clear signal as to who the Cubs plan to build their team around.
"This is just the base and the start of things to get these core players, those position players who you have control over for a long time and can stay here and be something special," Sveum said.
Castro, 23, wasn't surprised to see Rizzo get the large contract.
"I knew it was coming," Castro said. "If it happened to me, I think the next one was him."
Who's next? Castro wouldn't say. But Rizzo does give young players the same message.
"[The front office] has been watching me since I was 17," Rizzo said. "They've seen me develop, they've seen me make my mistakes, and they're going to continue to see me develop and do good things and bad things. What I tell the young guys is work hard. You can always control working hard. Once you get labeled as slacking off by one coach, that can stay with you for a long time. That's the message I try to send.
"Last year, at this time, I was in Triple-A and wondering when that call was going to come, and it's just the hard work pays off. Five years ago at this time, I was in a hospital waiting on my first treatment for cancer. It's crazy how everything has come full circle."
Now, the focus is on playing winning baseball.
"The only thing I think about is that: winning here," Castro said. "I know it'll be unbelievable. That's why those people up there started signing players for long-term deals, to be here when the team becomes good every season. I think it's very soon."