Both "will be welcome" and "will be welcomed" are correct. This is because 'welcome' can be both an adjective and a verb. In the first one, 'welcome' is an adjective. In the second one, 'to be welcomed' is a verb in the passive voice. I think the former is more natural. But neither of your sentences are very natural. You could say something like "I hope that our offer will be accepted", "I hope that our services will be welcome", "I hope that you will welcome our services" etc.

Thanks xarmanla! :)

I hope you will consider our offer and that you decide that our services meet your requirements.

Hi xarmanla. It is not a letter of employment. It is an offer letter of services.

I hope that you will accept our offer of employment.