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Morph as a verb is a recent coinage, but as as Google Books clearly shows, its usage literally shot up from the start and has increased constantly.

Morph: as a noun, in biology, 1955; as a verb, in cinematic special effects, c. 1987, short for metamorphosis. (Etymonline)

also, from Vocabulary.com, morph :

As a verb, it has only been around since the 1980s, when computers allowed animators to make things change shape in an apparently seamlessly way.

It appears from the above source that the verbal form was coined by a screenwriter or a videogame developer in the ‘80s, which, given the increasing popularity of the term, was probably a very successful one.

I couldn’t find more details about its origin, so can anyone help pin down when and by whom this verbal form first used, given the relative short history of the expression?

It looks to me like like the etymology is a little more complicated, with "morph" as a verb also being used early on in a gaming context at least as far back as 1982:

A staff of polymorph can help too if you morph him into something ‘easy’.
_{Re; Killing Umbers in net.games.rogue (Usenet newsgroup) 15 Sept.}

The game they're talking about here is Rogue (1980), and staffs of Polymorph are used to change monster type, which was probably based off the Polymorph spells from the pen and paper role playing game Dungeons and Dragons or its predecessor, Chainmail. Given that Chainmail was released in 1971, I wouldn't be surprised if there were earlier examples out there.

The OED doesn't have any other examples from before 1991. I was however able to find "morphing" in a computer graphics context in 1990:

Morphing Animation created by changing the shape of an object through gradual metamorphosis.
_{Amiga Resource, June 1990}

Morphology as a word has many generic uses however I am confining its use per question to its popular use within computing.

It had been applied to linguistic computer programs during the 1960's and used to produce new folklore e.g. "Propp's Morphology [of folklore] has been programmed for a computer (Dundes 1965)"

Most BBS of that era were text based and it was natural to hear the word applied in its more biological meaning from the [1800–1830] German root see https://en.wikipedia.org/wiki/Morphology_(biology)

1.the study of the forms of things.

the branch of biology that deals with the form of living organisms,

and with relationships between their structures.

In the early days of 1980's console programming the term morph was frequently used to describe changelings or transitions of one form to another.

Certainly when I was using sprites and early graphics programs "morphing" was
applied in many ways but "morph" accepted as a graphics term to mean change the form of something.

However there are many recent uses where the term morphology is still used to describe changing a maze or other game component / character much in the same fashion as "modding" is used to indicate modifications. see https://dysonlogos.blog/maps/vertical-morphology/

Many disciplines used the term freely and its seen as common usage by astronomers in 1970's here https://rd.springer.com/chapter/10.1007%2F978-3-642-20285-8_1

As others have pointed out it could have been a malaprop of metamorphosis but that word was not common hacker vernacular prior to the very late 80's when a number of academic papers started to reference metamorphosis.

The FACS system developed by Ekman up to the 70's was based as stated in "Facial Sign Facts Fantasies and possibilities" on "Morphology of facial expressions of emotions and their evolutionary basis" and the latest version 3 includes many references to morphing, however again I cant find a time where it uses the modern conception of meta.

Just my conjecture as I was not into RPG that it was initially popularised on games BBS. The term morph or morphing was frequently seen bandied about on other boards such as 3D modelling.

This morph of an international band is about 15 years old, can you guess the name of the group?