Hill was designated for assignment Friday, Sean McAdam of MassLive.com reports.
Hill struck out two over 1.1 relief innings in Thursday's 2-0 loss to Toronto.
The Red Sox selected Hill's contract from Triple-A Worcester on Tuesday, Chris Cotillo of MassLive.com reports.
The Red Sox are slated to call up Hill, Robert Murray of FanSided.com reports.
Hill walked one and struck out two over two scoreless innings for Triple-A Worcester on Friday.
Hill will start for Triple-A Worcester on Friday, Chris Henrique of Beyond the Monster reports.
The Red Sox signed Hill to a minor-league contract Friday, Rob Bradford of WEEI.com reports.
Hill said in an interview Wednesday with David Vassegh of AM 570 LA Sports that he has been ramping up during bullpen sessions and is preparing to sign with a team in August.
Hill plans to continue his playing career in 2024, Rob Bradford of WEEI.com reports.
Hill was placed on waivers by the Padres on Tuesday, Joel Sherman of the New York Post reports.