When Aaron Judge agreed to sign back with the Yankees, he was assured by Hal Steinbrenner the roster would be improved throughout the offseason.

The biggest move — after Judge — was the signing of Carlos Rodon, which was made official on Wednesday and comes with Judge’s seal of approval.

“One of the big questions I had, if I come back here for nine-plus years, was, ‘I want to be in contention every year, not just getting in the playoffs, but being a driving force in the postseason,’ ” Judge said he told Steinbrenner. “He backed up his commitment by going out there and getting one of the best pitchers on the market.”

Rodon will be introduced at a press conference at the Stadium on Thursday after his six-year, $162 million deal became official Wednesday.

They also made the signing of Tommy Kahnle official.

To make room on the 40-man roster for Rodon and Kahnle, relievers Lucas Luetge and Junior Fernandez were designated for assignment.

The left-handed Luetge has been a valuable arm the last two seasons for the Yankees, while the right-handed Fernandez was claimed off waivers from the Pirates last month.

Rodon is coming off back-to-back strong seasons, last year with the Giants and the season prior with the White Sox.

He’s battled injuries for much of his career, but when healthy, the 30-year-old has been excellent.

“What that guy has done over his career, especially the last two seasons, he’s a bulldog,’’ Judge said. “He’ll fit right into our mentality of being a winner. He oozes that confidence.”

Judge also pointed to the signings of Kahnle and Anthony Rizzo as reasons for optimism in The Bronx.

Steinbrenner said Wednesday he was pleased with the rotation “as long as we stay healthy, unlike last year.”

The Yankees continue to look for bullpen arms, as well as a left fielder.

With Andrew Benintendi gone to the White Sox as a free agent, general manager Brian Cashman said the team would look at internal candidates such as Oswaldo Cabrera and Aaron Hicks, as well as Estevan Florial, who has played well in the minors, but hasn’t proven himself in the majors.

Cashman added they’d also consider the free agent and trade markets.

“It’s an [area] we’d like to improve if we can, but if we can’t, we’ll go with what we have,’’ the GM said. “It’s been more of a challenge to solve.”

He also noted the loss of Benintendi’s left-handed bat in a righty-heavy lineup.

“It’s something we prefer, but at the same time, you can’t have everything you want at all times,’’ Cashman said.

Don’t tell that to the Mets, who managed to upstage the Yankees’ announcement of the Judge signing by inking Carlos Correa to a deal hours before that will bring their payroll to above $400 million.

Steinbrenner declined to put a number of where he wants his payroll to be.

“I do have a place I want to land,’’ Steinbrenner said. “Whether we’re there or not, I’m not gonna get into that. I can tell you we’re not done yet. I’d be surprised [if we didn’t make more moves].”

As for the Yankees’ main rivals these days, the Astros, Steinbrenner said, “They’ve had great teams and outplayed us in the postseason after postseason, but that can change.”