Feb 19 (Reuters) - Machinery rentals firm Herc Holdings HRI.N has signed a deal to buy H&E Equipment Services HEES.O for $3.83 billion, excluding debt, after H&E terminated its merger agreement with United Rentals URI.N, the companies said on Wednesday.

The cash and stock deal will combine the world's third- and fifth-largest firms that rent out machinery for construction sites.

United Rentals, which had entered into an agreement to buy H&E last month, later dropped out. Following H&E's previous agreement with United Rentals, Herc paid a termination fee of $63.52 million to United Rentals on behalf of H&E.

The buyout comes at a time when equipment rental demand is rising, as contractors find it more cost-effective to rent items such as pumps and air conditioning for their construction sites, rather than owning them.

H&E's shareholders will own about 14.1% of the combined company after the deal's completion, according to the terms.

Herc's offer of $78.75 in cash and 0.1287 shares of Herc common stock for each H&E share represents a premium of nearly 20% to the stock's last close on Friday.

The transaction was valued at $5.3 billion, including about $1.5 billion in debt, compared to United Rentals' $4.8 billion bid, which included debt.

The merged company is expected to gain around $300 million in annual EBITDA (earnings before interest, taxes, depreciation and amortization) synergies within three years of the deal being finalized.

The transaction is expected to close by mid-2025.

Founded in 1961, H&E provides a rental fleet including aerial work platforms, earthmoving equipment, material handling equipment and other general and specialty lines.

(Reporting by Kannaki Deka in Bengaluru; Editing by Pooja Desai)

((Kannaki.Deka@thomsonreuters.com;))