Smart Contracts on Bitcoin's blockchain Will projects build on top of Ethereum's blockchain be able to transit to Bitcoin's blockchain when the smart contract platform is up and running?
I would like to explain a bit the smart contract situation in bitcoin, as a "smart contract platform" is not a fixed wording in bitcoin world.  As such your question is not clear. Bitcoin already has smart contracts. A good summary was provided by Andrew Poelstra here. 

When you mention Ethereum, then usually solidity is used, which is "turing complete". People tend to state, that only turing complete machines are "real smart contracts". This is opinion based... Bitcoin has no plans to implement turing complete language, at least not directly. There is the concept of "Bitcoin Simplicity", and it's worthwhile to read the discussion thread in bitcointalk. There is also a link to the Simplicity white paper. 

Another development is going into side chains, like this.

A whitepaper for descreet log contracts is presented here.


  Will projects build on top of Ethereum's blockchain be able to transit
  to Bitcoin's blockchain when the smart contract platform is up and
  running?


At the current point in time, it is not visible, that people are working on making bitcoin compatible with ethereum smart contracts. It looks more like bitcoin devs are heading in a different direction, to avoid the problems of smart contracts with turing complete machines. When reading through the threads, you'll see how deep the politics are involved on this...