Let me share my opinion as Ukrainian citizen, from Kharkiv, eastern Ukraine.
On February 21, 2014 Yanukovych and the opposition signed an agreement on resolving the crisis in Ukraine, one of the conditions was the immediate (within 2 days) rollback to the Constitution of 2004, constitutional reform and early presidential elections no later than December 2014.
The same day, right after signing the agreement, Yanukovych left Kyiv even without driving home.
The next day in the interview Yanukovych said that he would not resign and is not going to sign the decision of the Verkhovna Rada, which it considers illegal, and what is happening in the country qualified as "vandalism and gangsterism".
Form this moment it was clear that he run away, made everybody fool, and was not going to do what he signed on February 21.
Actually, Yanukovych in unconstitutional manner withdrew from the exercise of constitutional authority and did not fulfill his obligations.
On February 23 Acting President Rights were assigned to Oleksandr Turchynov.
It was absolutely unclear where Yanukovych has gone.
The east of the country was under separatists attack. Yanukovich seemed to be somewhere there. Assigning rights to new temporary president was the only correct way to save the country.
So it was absolutely legal.