Almqvist described his decision to leave the party as "incredibly difficult".
Anna Hagwall from Rättvik in central Sweden will take over Almqvist's seat in parliament.
She was ousted from her post as the party's second vice president in 2009. She has previously indicated that she would be interested in joining parliament and denied rumours that she is in conflict with the party leadership.
Last month, the Expressen newspaper published a series of video clips showing Almqvist and two other Sweden Democrats, Kent Ekeroth and Christian Westling, embroiled in a drunken fight in Stockholm in the summer of 2010.
The video, shot by Ekeroth on his mobile phone camera, shows the three men hurling racist abuse at comedian Soran Ismail and others.
The clips also show the three top politicians pushing a drunken man and a young woman, using words like "darkie" and "whore" and wielding iron bars.
The first clip was published on November 14th. The same day, the 30-year-old Almqvist announced his resignation as the Sweden Democrats' economic policy spokesman.
He and Kent Ekeroth also lost their party committee posts.
Westling resigned as Stockholm city councillor and Ekeroth took a "timeout" as justice policy spokesman.
Ekeroth later said that he would step down permanently, but that he planned to keep his seat in parliament and would continue working for the party.
The question of whether Almqvist would remain in parliament has been in limbo, however.
The party leadership urged him to think "seriously" about whether to keep his seat. Almqvist said he needed time to think about his future but continued to participate in parliamentary votes.
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"After plenty of discussion we have together concluded that neither Erik nor the party would benefit from him remaining in parliament," Sweden Democrat party secretary, Björn Söder, told the TT news agency on December 30th.
"He has realized that it would be difficult for him to focus on politics after all that has happened. I think he has taken a very responsible decision," Söder added.
Sven-Olof Sällström replaced Erik Almqvist as economic policy spokesman and Richard Jomshof replaced Ekeroth as justice policy spokesman.
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