Zurich has always welcomed transients and exiles: Wagner, Lenin and James Joyce were all made comfortable here, conceiving their most important works sojourning in the placid Swiss-German-speaking city.

If the Brooklyn-born conductor David Zinman thought he too was just passing through, he was proved wrong.

This year's Edinburgh International Festival Brahms performances by the Tonhalle Orchestra in the Usher Hall, mark the modest but charismatic New Yorker's farewell after 20 years with Switzerland's oldest and most famous orchestra, 18 of them as principal conductor.

It has been an extraordinarily long and happy partnership by contemporary standards. This is not quite a farewell, as he will continue to conduct occasionally, but the French conductor Lionel Bringuier is poised in the wings "a new generation artist with energy enthusiasm and charisma" according to Zinman, who is working on a memoir of his long orchestral career in the US and Europe.

Since 1993, Zinman and the Tonhalle have been "one of those very special partnerships" according to Matthew Studdert-Kennedy, the Edinburgh Festival's artistic administrator. "Normally, if you last a decade with an orchestra you are doing exceptionally well."

"David has had time to develop a very broad repertoire, and it has all been quite strategic, he is not one to be rushed into things. He has wanted to do things in depth, a meaningful way, such as the Tonhalle's famous series of Mahler recordings, and Brahms symphonies. They have gone in depth into everything they do."

Zinman explains the success of the relationship with the orchestra in more human terms. "I always wanted to see how far I can go, and each step has taken me further along the road. I was there for them and they were there for me. I came at the right time and we grew together. I love the hall, I love the city and I like the musicians."

This most down-to-earth of maestros is the son of a Russian-born hardware store-keeper who emigrated to New York from Odessa to escape Czarist conscription.

Encouraged to study the violin by a fiercely ambitious mother, young David determined on his career while hearing a performance of Beethoven's Eroica symphony while a student at the New York High School for the Performing Arts ("You've seen the movie Fame? That one.")

"I think it's true to say that I am most proud of the incredible recordings I have been able to make with the orchestra, during my tenure. They have brought the level up to an international level, rivalling almost any of great international ensembles."

The judgment is, obviously, shared by the EIF. Studdert-Kennedy particularly loves the Tonhalle's "fantastically rich string sound works well in the Usher Hall. They felt very much at home from the first note, which is the same reason that many great orchestras love to return to play here."

That sound of the Tonhalle, named after its glorious neo-baroque lake shore concert hall, will be familiar to Edinburgh audiences from visits in 2009 and 2011.

This year's Brahms programmes are a delightful prospect to Zinman who, as the Tonhalle's recent CD release of Brahms symphonies attests, finds "something uniquely satisfying about his music...its blending of spontaneity and intellect. I've always felt a sense of rapport when conducting Brahms's music.

"We recorded the four symphonies and it was clear that both the orchestra and I had a wonderful time doing so."

The orchestra's special understanding with German music has been showcased this year by its part in the Wagner bicentenary events, in which Zurich has commemorated its role as "hothouse" to his genius, in the years from 1849-1858, when Richard and his wife Minna lived here, escaping the consequences of his revolutionary activity in Dresden.

On the run from the German police, Wagner found himself a patron, Otto Wesendonck, a wealthy young businessman who accommodated the Wagners in a house on the grounds of their idyllic hillside villa - now the Rietberg museum of oriental art. Wagner characteristically repaid the favour by flirting dangerously with Wesendonck's wife Mathilde, his "muse", leading to the Wagners expulsion from his Swiss paradise.

The Zurich Festspiele's Wagner celebration, and the Tonhalle's part in it, including Zinman's arrangement of relative rarities such as Wagner's Piano Lieder for Two Soloists, and Faust Overture in D Minor have been more probing and thoughtful than the customary adulatory Wagner events.

The Tonhalle's Wagner in Zurich CD, with Zinman conducting works that Wagner performed or conceived in the city, is one of the stand out recordings of the bicentenary.

It is Brahms not Wagner through which Edinburgh will witness the rich relationship between this orchestra and its principal conductor. The Tonhalle will be playing the Violin Concerto, along with Bruckner's Symphony No 3, and then two nights later, the mighty German Requiem, with the Swiss soprano Rachel Harnisch and Austrian baritone Florian Bösch, backed by the power of the Edinburgh Festival Chorus. Zinman knows the choir only by reputation.

"I have known it [EIF] for many years, and it is the diversity of the Festival which makes it unique, with all the orchestras, opera, and, in particular, the fantastic Fringe, which to me is as interesting as the Festival itself."

Brahms also seems an appropriate choice for Zinman's Festival farewell, as the composer is something of a musical patron saint of the Tonhalle, as well as to Zinman personally, who remembers buying tickets to the "bleachers" (cheap seats) to outdoor performances of the symphonies as a schoolboy.

It was Dr Brahms himself who in 1895 opened the 1455-seat Tonhalle, renowned for its wonderful acoustic, by conducting his own Triumphleid [song of triumph], a chauvinistic celebration of German victory over the French.

The evening was "not a wild success" according to Zinman, though it can't have helped the Great Man to work beneath a picture of himself on the Tonhalle's classical trompe-d'oeil ceiling. He is up there, with his old-testament beard, in an anachronistic pantheon alongside Beethoven, Wagner, Bach, Haydn, Mozart, Gluck and Liszt.

Zinman would never claim such prominence himself, but there will be concert-goers in the cosmopolitan Swiss city who might think, that after 20 years, in which the Tonhalle's international reputation has grown, that the conductor's shrewd, but jovial features should feature somewhere up there, among the cherubs and the clouds.

David Zinman conducts the Tonhalle Orchestra in the Usher Hall tomorrow and on Monday