A consultation on handing more powers to the City watchdog and the Pensions Regulator will be launched by the Financial Conduct Authority (FCA) in the spring.
However, most changes will not be made until the next parliament because the shake-up needs parliamentary approval.
Mr Hunt said the transparency drive would mean employers and savers “can see how their money is invested and how the returns compare to other schemes.”
Current rules are inconsistent and do not require funds to disclose detailed information about British investments. The overhaul would apply to so-called defined contribution (DC) schemes, where returns depend on stock market performance instead of salary averages.
The Treasury wants DC pension funds to disclose their levels of investment in British businesses, as well as their costs and net investment returns by 2027.
Mr Hunt said: “British pension funds appear to contribute less to the UK economy than international counterparts do as they invest less in our domestic businesses. These requirements will help focus minds on how to improve overall returns and outcomes for savers.”
UK returns have lagged behind overseas markets for decades and experts suggested the transparency drive may not lead to more investment in Britain.
Laura Myers, partner and head of DC pensions at consultants LCP, said: “Pension fund trustees need to be able to invest their members’ money where it will provide the best returns.
“More transparency is welcome, and many trustees would like to invest more in the UK if the right investments were available. Indeed, we have already worked with many schemes to add private market investments.
“But the most important focus must always be to deliver the best pensions for savers”.