The move will impact on 35 jobs, although some foundry operators will move to other roles.
The closure represents a significant moment in the history of the Ironbridge Gorge, bringing to an end centuries of iron production on the site and removing the last major industrial name from the Cradle of Industry.
Aga, which has consulted with union officials, said "everything possible" is being done to mitigate the impact of any compulsory redundancies, but said that the foundry is no longer economically viable.
The company's factory at Ketley will be kept open, with iron for the Aga ovens assembled there being sourced from other foundries across the UK and the EU which are not part of the Aga Rangemaster group.
Aga spokeswoman Laura James said: "The decision to close the foundry in Coalbrookdale has been made because it is no longer economically viable to maintain production.
"Product portfolio changes and reduced demand for cast-iron castings from sister companies within the group has significantly impacted on the plant’s ability to produce castings economically.
"Following an orderly and structured wind-down of manufacturing at Coalbrookdale, we will be sourcing our castings from a number of third-party suppliers both in the UK and across Europe.
"All assembly of Aga and Rayburn products, including the enamelling process, will continue to be undertaken at our main manufacturing site at Ketley, which also houses our product development teams.
"During this transition period we will ensure that the quality and on-time delivery of our products will continue as is it is today and that there will be no impact on our high levels of support and technical service. The closure of the foundry is part of a plan to improve efficiency and secure the longer-term future of the AGA brand and its manufacture in the UK."
Aga Rangemaster was sold to Illinois-based food services giant Middleby Corporation in 2015, in a deal worth about £129 million.
In the first quarter of the new financial year Middleby achieved net sales of about $516 million (£398 million), with earnings or profit of $70.7 million (£54.6 million).
While Aga's sales have fallen since the takeover, mainly because of unprofitable products being withdrawn and price discounting being eliminated, it has become more profitable because of synergies across the group allowing for cost savings.