I believe this was one of Bernie's request, when he met with Clinton yesterday...at least it is what I saw on the news last night when one of the stations was interviewing Debbie W and asked her if she would resign...he probably also has given a suggestion on who Hillary should pick.
Clinton is the head of the DNC as the nominee, but she is just presumptive nominee so I don't believe she could remove Debbie right now before the convention, without Obama's consent...? that's just speculating on my part, I have no inside information....AND I have not read the link yet.
Neither Clinton nor Obama could officially remove DWS as DNC Chair - only the DNC Chair committee can do that. Both of them probably have the cachet to get the process started, though - although I don't think they have.
DWS is still (on paper) the DNC Chair, but the presumptive Presidential nominee's campaign always takes over around this point in the cycle.