In a stock exchange notice on Friday (29 September), the board said the decision had been taken following capital allocation across the portfolio and pipeline, reflecting its material discount to NAV.
"The board believes that the current share price materially undervalues Syncona's portfolio and its prospects, and that the shares represent a compelling and unique investment opportunity," it said.
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The board added that the capital allocated to the buyback does not impact planned investment into the trust's investment pipeline over the next 24 months.
According to data from the Association of Investment Companies, the trust, which invests in a portfolio of life science companies and holds £1.2bn in assets, is currently trading at a 40% discount.
Melanie Gee, chair of Syncona, said: "The board of Syncona has a high level of confidence in our portfolio and its valuation - this is reflected in our decision to commence a buyback.
"We believe that purchasing up to £40m of shares allows us to strike the right balance between continuing to focus capital allocation on our maturing portfolio and a share buyback given the material discount to NAV at which the shares trade."
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As at the end of June, Syncona's capital pool was £613.1m. Since then, the trust has deployed £34.2m, taking total deployment across the portfolio in this financial year to £58.6m.
SYNC estimated that deployment into the portfolio and pipeline at the end of the financial year will be between £150-200m, in line with prior guidance and excluding the £40m earmarked for the share buyback.
Chris Hollowood, CEO of Syncona Investment Management, added: "The Syncona team has been focused on our long-term ambition to deliver net assets of £5bn by 2032 and we are working closely with our companies to guide their most promising assets to late-stage clinical development where we believe significant value can be accessed.
"We believe that current market conditions may also provide opportunities to allocate capital to clinical stage assets outside the Syncona portfolio. We look forward to providing the market with an update on the portfolio's progress and upcoming milestones at our interim results."
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In a research note, Peel Hunt analyst Miles Dixon said the buyback programme represents a "sensible use of capital".
"We are not usually supporters of share buybacks - thinking the returns and growth in healthcare are so compelling - but in this instance, where there are only a handful UK-listed companies where the mid- to long-term returns prospects are so clear and obvious to us, we believe this represents a sensible use of capital," he said.
"As a reminder, Syncona has delivered a c.21% IRR since 2012, a 1.5x multiple across its portfolio having generated £948m from four successful exits and currently trades on a deep discount to NAV of 40%."