John Podesta, a top White House adviser, will take on a senior role in Hillary Clinton’s emerging presidential bid after he leaves the administration in February, three people familiar with the matter said. The move is one of the most definitive signs yet that Mrs. Clinton is building the apparatus to launch a 2016 run.

Mrs. Clinton isn’t likely to announce her decision on whether to enter the race until the spring. But her advisers are making preparations for such a campaign, as evidenced by Mr. Podesta signing on.

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