Even before Jon Lester chose to sign with the Chicago Cubs late Tuesday night, the Boston Red Sox were exploring all their rotation options.

And it seems like they wasted little time in acting.

According to multiple reports, the Red Sox and Arizona Diamondbacks have agreed to a trade that will send left-handed starter Wade Miley and a minor leaguer to Boston for pitchers Rubby De La Rosa and Allen Webster.

Only hours after getting a goodbye call from Lester around 10 p.m. Tuesday – before it was learned the lefty had agreed to a $155 million, six-year contract with Cubs – Cherington lamented that he wished things had gone differently when Lester was still with Boston.

“I think we would have liked to have had more chance for dialogue prior to the season,” Cherington said Wednesday at the winter meetings. “Why that didn’t happen, maybe there’s more than one reason. I think we can certainly learn from the process. But we desired to have more dialogue prior to the season, and (we) made an effort during the season and weren’t able to.”

Lester had expressed interest last winter in re-signing with the team that drafted him in 2002. But after the Red Sox made in spring training a four-year, $70 million offer, Cherington said Lester and his agents were reluctant to talk again.

With the team falling in the standings, trading Lester to the Athletics at the July 31 trade deadline made perfect sense for Boston. At that time, Lester said leaving Boston didn’t rule out a return to the team next season.

But the Red Sox had a maximum contract offer in mind and it fell about $20 million short of the offer made by Theo Epstein, the Cubs’ president of baseball operations and former Red Sox executive.

“We were given every chance to get to where we were willing to go,” Cherington said.

Cherington said Tuesday Boston has spoken with pitcher Justin Masterson, who came up through the Red Sox farm system before being traded in 2009 during his second big league season. The right-hander went 7-9 with a 5.88 ERA for Cleveland and St. Louis this year, when he spent time on the disabled list because of a knee injury.

After finishing last in the AL East at 71-91, the Red Sox revamped their lineup by adding free agent position players Hanley Ramirez and Pablo Sandoval. They are now focusing on filling two rotation spots.

Lester, a three-time All-Star who turns 31 next month, was the clear first choice. With or without Lester, Cherington thinks results are what matters most.

“I think our fans expect us to deliver on the field and win games,” he said. “In order for us to give the best chance, we have to add to the pitching staff. There are all sorts of ways to do that. Of course there’s a connection to certain players more than others. But ultimately they care about the people we put on the field.”

In Miley, – a first-round pick in 2008 – the Red Sox will get a lefty who was 8-12 with a 4.34 ERA in 33 starts spanning 2011/3innings last season. He struck out a career-high 183 and walked 75.

Miley has thrown at least 194 innings each of the last three seasons, compiling a 38-35 record, 3.79 ERA and 1.32 WHIP in 106 career games (102 starts).

He was named an All-Star in 2012.

Webster and De La Rosa were acquired in August 2012 as part of the trade with the Los Angeles Dodgers sending Adrian Gonzalez, Carl Crawford and Josh Beckett to Los Angeles.

Lester also had been sought by the World Series champion San Francisco Giants and the Dodgers.

Now, Chicago has an ace to lead the rotation as it tries to end a run of five straight losing seasons and a championship drought that dates to 1908.

Lester’s contract contains an option for 2021 that, if it becomes guaranteed, would make the deal worth $170 million over seven seasons.

The average annual value of $25.8 million is the second-highest for a pitcher behind Clayton Kershaw’s $30.7 million as part of a $215 million, seven-year deal with the Dodgers that began last season.

After the deadline deal, Lester helped Oakland reach the playoffs for the third straight year before a 9-8, 12-inning loss to Kansas City in the AL wild-card game. He finished 16-11 with a career-best 2.46 ERA and 220 strikeouts last season and is 116-67 with a 3.58 ERA in his career.

“It’s not often you get to win the lottery, and we won the baseball lottery this year,” new Cubs manager Joe Maddon said. “Now it’s up to us to put it into effect.”