|Simplistic diagram of ATP as energy currency showing how the breaking of one phosphate bond can release energy (left arrow); whereas it takes energy to make ATP (right arrow).|
In 1941, German-born American biochemist Fritz Lipmann, in his “Metabolic Generation and Utilization of Phosphate Bond Energy”, although he did not use the term “money” or “currency”, began to outline the view how the bond energy stored in ATP could be used to pay for or run the energetics of (endergonic) reactions, that wouldn't normally go on their own. 
Beyond this, it is difficult to say who coined the term “energy currency”. The term commonly began to be used in 1970s in reference to English biochemist Peter Mitchell’s 1961 chemiosmotic theory of membrane energy transduction, which showed that ATP synthesis was coupled to electrochemical gradients.
In 1989, American biochemist Bruce Alberts stated the following: 
“Just as energy stored in an elevated bucket of water can be dispensed in small doses to drive a wide variety of different hydraulic machines, ATP serves as a convenient and versatile store, or currency, of energy to drive many different chemical reactions that the cell needs.”
This rule is has become a ubiquitous sort of biological linchpin of energy teaching in biology. Into the 1990s, it became dogma in nearly all biology textbooks.
In 2001, American biophysicist Donald Haynie, in his Biological Thermodynamics textbook, employed a bold face type is assigned to the opening (page four) statement that: "ATP plays the role of the main energy 'currency' of biochemical processes in all known organisms." 
In economic thermodynamics, there have been attempts to develop a type of global currency based on units of joules. The most significant attempt was the 1920s effort by American engineer Howard Scott to introduce the notion of “energy certificates” to replace money as a unit of value in the economy.
In recent years, on the ATP energy currency model, there have been attempts to model money as a type of human molecular energy currency, used to couple reactions between people or in society. One example is Russian bioelectrochemist Octavian Ksenzhek argument that money can be considered as a virtual form of energy, i.e. "virtual energy", and that energy coupling in social systems is mediated by materialized forms of energy, such as money; whereby the role of money in social systems may be compared with that of ATP in biochemical systems, both of which act as energy carriers.  Another example is American chemical engineer Libb Thims' assignment of anthropomorphic molecular forms of value, such as money, gold, diamonds, etc., as types of secondary field particles, i.e. entities that act to transmit the electromagnetic force of movement to human chemical reactions. 
1. Alberts, Bruce. (1989). Molecular Biology of the Cell (pg. 62). Courier Corporation.
2. Lipmann, Fritz. (1941). “Metabolic Generation and Utilization of Phosphate Bond Energy”. New York. In: Advances in Enzymology and Related Subjects – Vol. 1 (1941), (pg. 99-162). Interscience Publishers.
3. Fezer, Harold. (1938). “The Energy Certificate”, Technocracy Pamphlet, Series A, number 10, July.
4. Ksenzhek, Octavian S. (2007). Money: Virtual Energy - Economy through the Prism of Thermodynamics. Universal Publishers.
5. (a) Thims, Libb. (2007). Human Chemistry (Volume One), (preview), (Google books). Morrisville, NC: LuLu.
(b) Thims, Libb. (2007). Human Chemistry (Volume Two), (preview), (Google books). Morrisville, NC: LuLu.
6. Mitchell, Peter (July 1961). "Coupling of phosphorylation to electron and hydrogen transfer by a chemi-osmotic type of mechanism". Nature, 191: 144–8.
7. Haynie, Donald T. (2001). Biological Thermodynamics (pg. 4). Cambridge University Press.
● Energy currency – Appropedia.
● The Cell’s Energy Currency – CliffNotes.com.