The board also opted to recommend use of election night results in a Franken-leaning Minneapolis precinct where 133 ballots went missing, a decision that could have cost him 46 votes if it had gone the other way.
"It was a great day for democracy," Franken attorney Marc Elias said after a hearing that drew protesters urging use of rejected absentee votes.
Franken had fought especially hard to include the absentees as he tries to overtake Republican Sen. Norm Coleman in the drawn-out recount.
Coleman's campaign lawyers said they would go to court over the absentee ballot ruling.
With all precincts recounted, Coleman has a 192-vote edge over Franken - down slightly from his 215-vote lead entering the recount.
But there's a long way to go. That margin doesn't include the absentees. Nor does it include any of the 6,655 ballot challenges the two campaigns filed during the recount. Both sides have withdrawn hundreds, but the state Canvassing Board will tackle some 4,200 starting Tuesday.
The board's decision on improperly rejected absentees doesn't guarantee they will be opened and counted because it doesn't have the power to order counties to do so. Most counties have gone forward with a voluntary sorting, though others have balked.
But Secretary of State Mark Ritchie said he's not worried about getting counties aboard.
"They are sobered and they would like to correct those errors," he said.
Coleman's campaign planned to file a petition with the state Supreme Court as soon as Friday to seek uniform rules for dealing with the absentee ballots, arguing that leaving the task to counties would create inconsistencies.
Coleman lawyer Tony Trimble said the campaign is asking counties to hold off on any action involving the ballots until the court weighs in.
At least 638 absentee ballots are known to have been rejected for something other than the four legal reasons for disqualification. That's based on an assessment of about half of Minnesota's counties by the secretary of state's office. State officials estimate the total could top 1,500.
It's not known which candidate stands to benefit most from those ballots.
"It would be unjust and disrespectful to those voters not to count those votes," said Judge Edward Cleary, one of four who sit with Ritchie on the board.
About 30 demonstrators gathered outside the Capitol hearing room to urge Canvassing Board members to count the absentee ballots. They held handmade signs saying "Let the people's votes count" and "Count every vote." Some wore "Count every vote" stickers.
The board acted after receiving a legal opinion from the office of Minnesota Attorney General Lori Swanson, a Democrat, that the ballots should be counted.
"There is no doubt that voters who have complied with all legal requirements, but whose ballots were improperly rejected, should have their vote counted," it read.
The opinion laid out several options for getting the ballots into the count, some involving court action and others through administrative means. It says that the campaigns are free to seek court orders to compel counties to take part.
The board voted unanimously to rely on tapes from a ballot counting machine rather than results from the manual recount in a precinct in the University of Minnesota area in Minneapolis. Coleman's campaign had argued against using anything but the recount figures.
A packet of ballots from the precinct couldn't be found after an exhaustive search of the city's elections warehouse. Consequently, the recount showed 133 fewer votes than the number of people who signed in on Election Day or who voted absentee.
Because Franken decisively won the precinct, he stood to lose the most votes if the board went with the recount tally over the machine tapes.
Associated Press writer Martiga Lohn contributed to this report.