I've been thinking about rebarreling my 7mm Rem Ruger 77 Mk II to a .338. I've already got a .338, and although I love the cartridge, but I don't really like the .338 rifle I have right now.

What is required to do this? Is it a simple barrel exchange, or do I need to do other stuff to the gun?

It should be a simple barrel swap since your gun is already a belted mag. Of course the headspace will have to be adjusted to the Ruger action too. While your have the barrel off that Ruger I would recommend that you have the lugs lapped & square the receiver.
Who's barrel do you intend to use? I have been using Lothar Walter barrels exclusively for the past couple of years and REALLY like their performance. By the way they offer 26 different barrel contours to choose from.

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NRA Life member

You may have to open up the barrel channel on the stock also depending on what contour you use. PS, I called Ruger once to do the same with my Model 77 they will only replace the barrel in the original caliber so its a custom barrel from one of the many makers.

Sounds like a straightforward rebarrel. As far as barrels are concerned I use Shilen and Douglas and like both. Another favourite are the barrels from Ron Smith in Alberta. I really like his barrels. They are cut rifled and as good as any. He also offers gain twist barrels for something a little different. Iam shooting 3 of them now and all are very good. Regards, Bill.