La referencia a un concepto amplio como es el de “relación jurídica patrimonial” permite precisamente asignar al contrato una función que no está circunscrita únicamente al campo de las relaciones obligatorias sino a cualquier tipo de relación jurídica que, siendo o no una obligación, tenga contenido patrimonial.
http://www.estig.ipbeja.pt/~ac_direito/civ_art47.pdf

a contract is an agreement between two or several parties, by which the parties establish, regulate or terminate a reciprocal legal relationship.

el contrato es el acuerdo de dos o más partes para constituir, regular o extinguir entre sí una relación jurídica patrimonial

http://eur-lex.europa.eu/Notice.do?mode=dbl&lang=en&ihmlang=...

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“Artículo 1351º.- Noción de contrato El contrato es el acuerdo de dos o más partes para crear, regular, modificar o extinguir una
relación jurídica patrimonial.” En efecto, el Código Civil dispone que el contrato crea, regula, modifica o extingue una relación jurídica patrimonial. Pero ¿qué es una relación jurídica patrimonial?.
Una relación jurídica es el vínculo que se genera entre dos o más personas en el cual una asume una obligación frente a la otra, que como contrapartida, tiene un derecho a exigir el cumplimiento de la obligación en cuestión. Esta relación jurídica será patrimonial cuando el contenido
de la obligación sea, justamente, de carácter patrimonial o económico.
http://www.aempresarial.com/web/revitem/43_14775_45226.pdf

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"legally binding relationship" could work.

An unwritten, unspoken contract, also known as "a contract implied by the acts of the parties", which can be either an implied-in-fact contract or implied-in-law contract, may also be legally binding. Implied-in-fact contracts are real contracts under which the parties receive the "benefit of the bargain". However, contracts implied in law are also known as quasi-contracts, and the remedy is quantum meruit, the fair market value of goods or services rendered.
http://en.wikipedia.org/wiki/Legally_binding

Or "quasi-contractual relationship"
Blacks Law Dictionary 1276 (8th ed. 2004). A quasi-contractual relationship is one implied-in-law where an actual contract does not exist.

http://www.gpo.gov/fdsys/pkg/USCOURTS-orb-6_08-ap-06196/pdf/...

A quasi-contract (or implied-in-law contract or constructive contract) is a fictional contract created by courts for equitable, not contractual, purposes. A quasi-contract is not an actual contract, but is a legal substitute formed to impose equity between two parties.
http://en.wikipedia.org/wiki/Quasi-contract


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Black's Law Dictionary Ninth Ediction
It is a quasi-contractual relation formed by the operation of legal rules and not by the agreement of the parties. Also termed agency from necessity.

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Quasi-Contractual Obligation Law & Legal Definition
Quasi-contractual obligations are regarded by law as contractual though they are not so in fact. Quasi-contractual obligations also include those obligations which are in fact delictal or tortuous and not contractual, but if the person wronged so desires, s/he may treat them as contractual and sue the wrongdoer for a breach of contract.
http://definitions.uslegal.com/q/quasi-contractual-obligatio...

Difficult question. Various authors use this though.

eg

http://books.google.co.uk/books?id=yNCHhbXpbKEC&pg=PA22&lpg=...

Self-Sufficiency of Law: A Critical-Institutional Theory of Social ... - Page 138 - Google Books Result
books.google.co.uk/books?isbn=9400742983
Mariano Croce - 2012 - Law
... the instance-rule of the contract (i.e. the agreement among two, or more parties , meant to set up, regulate or extinguish a legal patrimonial relationship) ...

[PDF]
CHAPTER 1. CONTRACT
www.legiscompare.fr/site-web/IMG/pdf/9._CH_1_Contrat.pdf‎
agreement between two or several parties to create, regulate, or extinguish as amongst each other a legal patrimonial relationship »65. Article 1174 of the Civil ...

[PDF]
BULLETIN - Posse Herrera Ruiz
www.phrlegal.com/wp-content/themes/twentyeleven/.../10-2008...‎
Oct 1, 2008 – regulation or termination of a legal patrimonial relationship between them and, except as otherwise stipulated, it shall be deemed to be exuted ...

etc.

I don't think there is a better definition around.