Westmoreland joins the team after WFR Honda announced its withdrawal from the series while Kirkham joins after a season with the factory-supported Samsung Honda team.
Buildbase BMW finished the 2012 season with Barry Burrell and Peter Hickman at the helm and the former secured a season-best for the team by finishing fourth at the season finale at Brands Hatch.
Hull's Westmoreland finished seventh in the title standings last year.
"I'm really happy to part of the Buildbase BMW team with official BMW support to challenge for the 2013 Championship. I have known the team for a number of years and now is the correct time to work together and I think we can put together a strong season," the 24-year-old said.
Team boss Stuart Hicken was delighted with his new rider line-up.
"We are feeling very positive about 2013 and are really looking forward to working with our new riders. James Westmoreland has shown he is a fast, crafted rider and I have admired him for some time so to be able to sign him was great for the team, especially as he came so close to the Showdown this season.
“JK impressed me with his desire to ride with the team and with his experience of the BMW he will make it a strong line up in our garage. We feel that the BMW is capable of running at the front and aiming for podium finishes so we want to hit the ground running next year."
Kirkham recorded his second career victory in the series in the opening race of last season at Brands Hatch.
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