Legislative leaders announced a compromise Monday to tame soaring health care costs that would make Massachusetts the first state to try to limit how much providers and insurers could spend on medical care.

The plan—likely to be voted on by the House and Senate on Tuesday, the final scheduled day for passing legislation – would allow health care spending to grow no faster than the state economy overall through 2017. For the following five years, spending would slow further, to half a percentage point below the growth of the state’s economy, although officials would have the power under certain circumstances to soften the target.

Supporters believe the bill will help moderate increases in consumers’ and businesses’ insurance premiums, but sticking to the cap could be a significant challenge for the state’s robust health care industry. Medical spending in Massachusetts in recent years has climbed 6 percent to 7 percent annually, compared with the state economy’s annual growth of about 3.7 percent. Health costs appear to be increasing more slowly in the past couple years, however, in part due to the economic slowdown.

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The bill was negotiated by three House and three Senate leaders after their chambers passed different cost control bills. If the House and Senate approve the legislation on Tuesday, Governor Deval Patrick would have 10 days to act on the bill. He has been in close discussions with legislative leaders on key issues, so he is unlikely to be surprised by major provisions.

For the most powerful hospitals and doctors groups, the outcome could have been worse. Some of the most stringent limits on providers passed by the House did not survive, including a luxury tax on hospitals, doctors groups and others that charge considerably higher prices than competitors. A separate House provision that would have required hospitals in systems to negotiate prices with insurers individually, rather than as a more potent group as is now commonly done, was also eliminated from the final bill.

The legislators, though, did include a provision proposed by Patrick to attack the market power of providers who can demand high prices for their services because or brand-name or geographic dominance, one of the most-cited reasons for rising medical spending.

The administration would be required to conduct a “cost and market impact review’’ of certain providers, including those trying to expand and those that do not meet the state’s spending benchmarks.

If the review finds that the provider has dominant market share, and has “materially higher’’ prices and total medical expenses than competitors, then the administration must refer the case to Attorney General Martha Coakley’s office for possible formal investigation.

The bill also includes provisions to reduce malpractice lawsuits, enhance public health and increase cost transparency for consumers.