I had a customer propose this same thing a couple of years ago. Yes, it can be done.
As others have pointed out, it does involve a lot of other work, and that runs the cost up to the point where you can almost buy a Weatherby and trade the 25-06 towards it to reduce the cost even further. Barrel ($450ish), open the bolt face ($100-ish), open the feed rails ($50-ish), reblue ($100), guesstimate about 200 fps extra velocity at best (check the ballistics tables). Compare that to trading and buying a new Weatherby ($1200 for the Weatherby and maybe $300ish trade-in).
So you may ask, "what did his customer decide to do?" Good question! We barreled the rifle in 6mm-06 with a 1:7" barrel and loaded up 115 gr Bergers that launched at 3400 fps, faster and flatter than the 25-06. Totally different direction, but it works.