Hamer will be familiar to Scotland's fans as the man who controversially sent off defender Gary Caldwell in the country's 4-0 World Cup qualifying defeat by Norway last year after booking him twice in the first half.
The Scottish FA said Hamer and two compatriots would take charge of Celtic's home game against Inverness Caledonian Thistle on Saturday and then travel north-east for Rangers' trip to Dundee United on Sunday.
Champions Rangers lead Old Firm rivals Celtic by three points after 14 matches.
Referees from Portugal and Israel will take charge of the weekend's other four Scottish Premier League (SPL) games with Malta's Marco Borg acting as fourth official at Kilmarnock's home game with Aberdeen.
An SFA spokeswoman said all SPL games were on despite the sudden withdrawal of planned Polish replacements on Friday.
The Scottish Football League (SFL), which oversees the three divisions below the SPL, called off Saturday's game between Greenock Morton and Falkirk.
"This is as a result of the recent withdrawal of the match officials who were designated for this match," the SFL said in a statement.
Saturday's three other SFL first division games had been postponed already after lots were drawn to see which of the four games, apart from the Challenge Cup final, would be allocated foreign referees.
The Polish Football Association said their officials, called up after Scotland's category 1 referees called a strike in protest at abuse from players and managers, would not be available after all.
"Because of the national league, after consultations... the Referees' Collegium of the PZPN (Polish FA) has scrapped the trip of its referee teams to Scotland," the body said on its website.
SFA chief executive Stewart Regan has called the referees' decision to boycott the weekend's matches "a very sad day for Scottish football" and said the fans, clubs and sponsors will suffer.
Neil Doncaster, the SPL chief executive, said in a statement on Thursday the Scottish Premier League was sympathetic to the referees' complaints and was disappointed an agreement had not been reached to call off the strike.
"The way to address concerns is through dialogue, not to walk away from the situation," he said.
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