Selim Eskelin passed away leaving no family of his own. In his will and final testament, he left his household effects and miscellaneous funds to his relatives. The rest of his estate went to the establishment of the Selim Eskelin foundation, whose purpose was to provide housing and scholarships for gifted students of the Sibelius Academy, formerly the Helsinki Conservatory. The leadership was to consist of three members elected from the Bank of Finland’s board of directors, The Finnish Organist Association and the Helsinki City Council, each serving a three-year term. The rules of the foundation were approved by the Ministry of Justice on 11th October 1938, and it was subsequently entered into the national foundation registry on 18th November 1939.

According to his will, the foundation's funds were to be held as a bank deposit. At the time of his writing, Eskelin could not have foreseen the strong inflation caused by the Second World War, which reduced much of the deposit's value. In addition, the foundation came into a piece of land in central Kotka and three-quarters ownership of another. The will strictly forbade selling the plots, but the rental income from the old wooden buildings on them was barely enough to cover their upkeep. The rules were not amended until 1969, when the foundation decided that its funds could be invested in securities and bonds. The old buildings were demolished, and the land was rented out for property development. This gave the foundation the means to carry out its founder's final wishes.

The Selim Eskelin Foundation's first scholarship of 1,000 Finnish marks was awarded to Tuomo Nikkola on 29th November 1974. The first accommodation for housing students was purchased in 1986, and following refurbishment its first tenant moved in on 1st December 1986.