Melrose, which buys underperforming manufacturing businesses and turns them around before selling them, said it would pay $20.50 for each Elster American depositary share, at a 43 percent premium to the average price in the last six months.
"We believe that Elster is an excellent fit with the Melrose acquisition criteria," Melrose Chief Executive Simon Peckham said.
"Elster is a high quality business with strong end markets and the potential for significant development and improvement under Melrose management."
Melrose said the deal had the backing of around 64 per cent of Elster shareholders so far. The tender offer is expected to start early next month.
"We are pleased to reach agreement with the Elster administrative board, who are recommending our offer," Melrose Chairman Christopher Miller said.
"Since flotation in 2003 we have created over £1bn of shareholder value and we believe that this acquisition gives us further opportunity to continue our track record of creating significant value for our shareholders."