If the population within a region of Ukraine wanted to become a part of Russia (suppose a fair vote was 75% in favor), is there a peaceful legal/government procedure in Ukraine to make this happen? Assume Russia is welcoming.
This would require a constitutional amendment:
The sovereignty of Ukraine extends throughout its entire territory.
Ukraine is a unitary state.
The territory of Ukraine within its present [ie 1996] border is indivisible and inviolable. (source)
Now, as this is part of Chapter 1, it could only be amended by a 2/3 majority in the Verkhovna Rada, followed by a referendum in the whole of Ukraine, not just the secessionist region.
Moreover, Article 157 states:
The Constitution of Ukraine shall not be amended, if the amendments are [...] oriented toward the liquidation of the independence or violation of the territorial indivisibility of Ukraine.
So an amendment to cede part of the territory to Russia would itself be unconstitutional, and the Supreme court has the explicit power to rule that any discussion in the Ukrainian Parliament is unconstitutional. It seems likely that even discussion to remove the restriction in 157 would be "oriented towards violation of the territorial indivisibility". The writers of the constitution tried very hard to make Article 2 unamendable by any constitutional process.
Of course, the constitution is only a piece of paper; it isn't self-enforcing. The government and people of Ukraine could simply ignore the constitution, or make no attempt to enforce it - laying claim de jure but allowing secession de facto. However, I would not call this a "procedure", rather the inherent fact that state boundaries are not natural but defined by humans.