He grew up in the southern city of Beer Sheva in an immigrant absorption camp (Ma'abarot) and later in government subsidized housing.

He earned his PhD in environmental engineering at the Johns Hopkins University in 1989 under the direction of Professor Charles R. O’Melia.

In 1998, Elimelech accepted a position at the Chemical Engineering Department at Yale University as the Llewellyn West Jones Professor.

[6] Elimelech authored invited perspective articles that helped to shape the research and engineering practice in water purification and desalination.

Specifically, he advanced the use of ultrahigh-pressure reverse osmosis (UHPRO) as a technology to displace energy-intensive thermal evaporators that are commonly used for brine management).

Elimelech’s pioneering research on another desalination technology, the forward osmosis (FO) process,[14][15][16] has also impacted the water industry.

He developed theories and models for concentration polarization in membrane separations, providing analytical expressions for predicting water flux.

[28][29] The paramount role geochemical heterogeneity in the form of iron oxide coatings on mineral grains was introduced, verified in laboratory and field experiments, and incorporated in transport models.

Specifically, he demonstrated the incorporation of nanomaterials into membrane technologies for fouling control, performance enhancement, and energy savings,[32] as well as the development of point-of-use filters for virus removal and inactivation.

[33] Notable among his works is the demonstration and elucidation of the mechanisms of bacterial inactivation by carbon nanotubes[34][35]  and graphene oxide,[36][37] which was later applied to membranes and water filtration.

Elimelech and his group developed a multiwalled carbon nanotube filter for the removal and inactivation of pathogenic viruses and bacteria from polluted waters.

[40] He was the first to point out that research on ultrahigh water permeability reverse osmosis membranes will have negligible impact on energy consumption in desalination.

[41] Elimelech demonstrated the relative insignificance of advanced materials in enhancing the energy efficiency of desalination technologies, while proposing more effective materials-based and process-level research directions.