Joshua Baez, the onetime standout baseball player at two Boston high schools, Cristo Rey in Dorchester and the Snowden International School in the Back Bay, moved one big step closer to his goal of playing in the major leagues on Monday when he signed a contract worth a reported $2.3-$2.5 million with the St. Louis Cardinals of Major League Baseball’s National League at the team’s home park, Busch Stadium.

He had earlier committed to play at Vanderbilt University, an NCAA Division One baseball powerhouse. For choosing them over academia at this point, the Cardinals included the cost of tuition to pursue an undergraduate degree in the contract, according to the St. Louis Post-Dispatch.

The 6-foot-3, 230-pound Baez, a native of Boston who spent his early years (to age 11) in Santo Domingo before coming back to live in Dorchester, turned 18 last month and closed out his high school career this spring as a senior standout at the Dexter Southfield School in Brookline where he pitched (a 1.94 ERA) and played outfield and batted .378. He was a member of the Boston Blue Jays of the Boston Park League until he was drafted.

“I’m just glad to be here,” he told reporters after a round of batting practice at the stadium. He will now join the world of the minor leagues at the Cardinals’ facility in Jupiter, Florida. “For now, it’s just about getting better, continuing to work on it,” he added.

The following is what he needs to work on, per Baseball America’s scouting report on his prospects as cited by the Post-Dispatch:

“He performed well last summer on the showcase circuit and he started the spring by managing his at-bats well, but as the season progressed, he got more out of sync and swung through a lot of ordinary Massachusetts high school pitching. Baez isn’t a free swinger, but there’s some stiffness to his stroke and he tends to get his front arm extended early, which hampers the adjustability of his swing to be able to react to and square up different pitch types and locations. In center field, Baez shined all spring. He’s a solid-average runner underway who doesn’t have typical burner speed or long gliding strides for the position, but he’s a power runner who has good instincts, reading the ball well off the bat with good routes to both gaps. He’s built like a corner outfielder and many scouts believe he will ultimately outgrow the position and head to right field, but he has enough athleticism and ball skills to start out in center.”

And so begins Joshua Baez’s hopeful trek to the bigs, under the watchful, discerning eyes of those scouts and the prayers of his fans in Dorchester, the Back Bay and Brookline.

In the meantime, though, there’s that house he said he’s going to buy for his mother. That’s a big deal, too.