First, the descriptive history, then an attempt at explanation.
The OED gives definitions in historical order, the meaning that appears first comes first, and later meanings come in order. Other dictionaries, like learner's dictionaries, may choose other orderings like most common meaning first.
The first entry for 'accede' is
- intr. To come forward, approach, or arrive (at a place or state). Also: to come into being. Obs. First attestation 1465.
No one uses 'accede' in this way now (therefore the designation 'obsolete') but it is closely related to 'accession' as in OED's fifth entry, taking on a position or role.
OED's third entry accords with the current usual meaning of 'to yield':
- intr. To assent, agree, give way. Usually with to, †unto. First attestation 1534
So currently, the English word has roughly the same meaning as the Spanish version.
During the late Middle Ages and early Renaissance, all the European countries were, along with expanding literacy, expanding their vocabulary, a lot of it with Latin origins (easier for the Romance languages). The etymology for 'accede' at OED (etymonline's version, which is usually taken from OED, strangely only addresses meaning 1) is complicated.
It was borrowed, as is usual for such formal latinate terms, from Anglo-Norman/Middle French (the language of the 1066 conquerers) where it meant accept or agree, close to 'yield', the modern English or Spanish meaning.
So in some sense your question is really about why English borrowed the meaning 'to come forward, approach' first but then later went back to the classical Latin/French/Spanish version.
'Why' questions are hard to answer definitively (there's usually no reliable evidence about internal motivation), so I can speculate that probably the first English scholar (most likely well-versed in Latin) used the word very metaphorically, the Latin 'accede' meaning 'yield' being used expansively to mean to approach, the other person allowing one to approach. This is a bit of a stretch, but I think no more of a stretch than using 'received' to mean 'accepted as authoritative'
For quick reference, OED's etymology entry for 'accede'.
< Anglo-Norman and Middle French acceder (French accéder ) to approach (1270 in Old French in an isolated attestation, subsequently from 1470), to accept (something), to agree (to something) (14th or 15th cent. in Anglo-Norman; this sense is unparalleled in continental French until later: see below) and its etymon classical Latin accēdere to go or come (to), draw near, approach, to enter, to resort (to), to attach oneself, join, to agree, assent, to be added, constitute an addition, accrue, in post-classical Latin also to attain to (a dignity) (11th cent. in a British source), to perform, fulfil (an office) (12th cent. in a British source) < ac- ac- prefix + cēdere cede v. Compare Italian accedere (a1250).
The (continental) French verb is first attested later in uses corresponding to senses 2 and 3, and originally as a legal term: 1731 in accéder à with specific reference to agreeing to a treaty (compare the similar use in quot. 1830 at sense 2), 1771 with specific reference to agreeing to a contract of sale. The general sense ‘to accept, agree to (something)’ is first attested in French in 1790.
