Hompesch was born in the village of Bolheim, now part of the town of Zülpich in the Eifel region.

For this, he needed to obtain a dispensation from the Holy See, serving as a page to the Grand Master Manuel Pinto da Fonseca.

In late 1775, Hompesch was appointed as the Order's ambassador at the court of the Holy Roman Emperor in Vienna, a post he held for the next 25 years.

In 1776, he was raised to the rank of Knight Grand Cross, making him a member of the Standing Council of the Order.

[1] In the following years, he received charge of the commandery in Rothenburg (1777), followed by those in Herford (1783), Basel and Dorlisheim (1785), Sulz, Colmar and Mülhausen (1786) as well as Villingen, in the Black Forest (1796).

In 1798, Hompesch was warned that the French fleet that was sailing to Egypt under Napoleon Bonaparte intended to attack Malta as well.

Bonaparte demanded free entrance to the harbour for the entire fleet with the rationale being to gain water provisions.

The following day a treaty was signed by which the Order handed over sovereignty of the island of Malta to the government of the French Directory.

In return, the French Republic agreed to "employ all its credit at the Congress of Rastatt to procure a principality for the Grand Master, equivalent to the one he gives up".