Senzel elected free agency Wednesday, James Fegan of SoxMachine.com reports.
The White Sox designated Senzel for assignment Monday.
Senzel is out of the lineup for Wednesday's game against the Athletics.
Senzel is out of the lineup for Monday's game against the Rangers.
Senzel is not in the starting lineup against the Royals on Saturday.
Senzel is in line to be the primary second baseman for the White Sox, Vinnie Duber of AllCHGO.com reports.
Senzel agreed to a contract with the White Sox on Tuesday, Jon Heyman of the New York Post reports.
The Nationals requested unconditional release waivers for Senzel on Friday.
The Nationals designated Senzel for assignment Saturday.
Senzel is out of the lineup for Wednesday's game against the Mets.