welcomed : man wird bereits begrüßt.
welcome: man ist herzlich eingeladen, aber noch nicht eingetroffen.

Würde ich so nicht unterstützen. Abgesehen von dem sehr verbreiteten 'You're welcome' für 'Bitte', das sich ja auch nicht auf die Zukunft bezieht, würde ich auch in z.B. diesem Satz kein -ed verwenden:

What's that?
Cow's foot.
Oh, I've never had those.
Well, you're very welcome to try them.

Ich finde den ganzen Satz allerdings etwas seltsam. Gibt's eine deutsche Vorlage?

When you're inviting someing to eat something, I'd drop the "warmly" bit. It sounds quite odd.

edit: see #2

Ja - Kontext... :-)
Jemand anderer (native) hat die 'welcomed' Variante verwendet, also mich auf ein Häppchen eingeladen. Persönlich hätte ich, als Nicht-Native, es mit 'welcome' formuliert (und wohl ohne 'warmly').

Edith: native BE! :-)

Given the context, it still sounds odd to me, yet it is plausible. Perhaps rather old fashioned and hyper-polite.

'odd' bezogen auf 'warmly' oder auf 'welcomed'? :-)

"warmly" is odd and "welcomed" in this context is IMO nonsense. Are you sure that's what you heard?

Ich hab's per E-Mail bekommen. Insofern ist ein Verhören nicht möglich. :-)

In that case, perhaps "welcomed" is a typo or there's some other explanation. As someone who lived in GB for quite a few years, I don't recognize it as standard BE.

This is the relevant part of the entry in the online Oxford:

[predicative, with infinitive]
Allowed or invited to do a specified thing:
we arrange a framework of activities which you are welcome to join

Please feel welcome to come and join in, if you enjoy singing, or just enjoy the sound.
All current members and interested community members are encouraged and most welcome to attend.
People can express any opinion or concept they desire and anyone is welcome to take part.
http://www.oxforddictionaries.com/definition/...

I think "welcomed" is grammatically OK - it is a passive construction, like "you are invited".
In "you are welcome", welcome is an adjective, as in "Smokers / Bikers welcome".

Having said that, I still think neither sentence is particularly good.
I'd probably say You're welcome to (have a) bite of xx - it's not up to me to say whether that person will actually enjoy xx.

I think the right word for the OP is "welcome," and the problems there are the odd-looking "warmly" and "enjoy."

This, for example, would work:

"You are very welcome to try our pigeon-poop pancakes."

There is a standard phrase "warm welcome," but it is used in a sentence such as "We received a warm welcome from the prime minister."

Note that "welcome" is a noun in the above example.

You could also say something like "I gave them a warm welcome." But it sounds odd to say "you are warmly welcome." For one thing, it's really not for you to say to the person you are welcoming how warm your welcome is at the time that you are extending it.

I agree that "invite" is the word you want here, as in "You are cordially invited to ... ."

Sowohl warmly als auch welcomed hört sich für mich unidiomatisch an.

Welcomed geht in Sätzen wie:
The foreign delegation was welcomed by the President.
The President welcomed the foreign delegation.
Nicht im OP. Die Vergangenheitsform welcomed beißt sich mit dem are.

@ MBSHU.
Die Vergangenheitsform welcomed beißt sich mit dem are

This is a passive construction, like your first sentence. The "you" in the OP is not the subject of the sentence, and welcomed is not the past tense but the past participle.

Compare:
Cricket is played in Australia.
The culprits have been punished.
The foreign delegation was welcomed by the president.
The pizzas will be delivered to your door.

@tomtom: What you say about the verb to welcome as used in the passive is correct. However, IMO, the OP is not about the verb but about the predicative adjective welcome, as in "You are welcome to use my laptop if you don't have yours with you," or "You are welcome to have dinner with us when you get here."

(Sorry if you've already made that distinction yourself and I've overlooked it.)

Re #16:
I agree entirely. I was just saying that "you are welcomed" is not grammatically incorrect. I certainly made the distinction in my head, but haven't actually posted it here very clearly, probably because I don't think the sentence works very well either way.