Over 1,000 people had already moved to the centre, a vast hangar close to the border, on Tuesday night.
But according to Minsk, around 800 others had remained outside even as temperatures dropped below freezing, spending the night in tents or around campfires.
These last had now also moved because weather conditions had deteriorated further, the border guard said, adding that at the centre the migrants had received “hot meals, warm clothes and basic necessities”.
The Polish border force confirmed the evacuation of the camp, which had been set up in a wooded area not far from the border post of Brouzgui.
On Tuesday, hundreds of migrants faced off against Polish forces, who used tear gas and water cannon, at the crossing point.
The relocation comes after weeks of rising tension between Belarus and the European Union.
The European Union accuses Belarus strongman Alexander Lukashenko of luring the migrants—mainly Iraqi Kurds—to the border as revenge for sanctions slapped on his regime after its suppression of opposition protests last year.
Lukashenko and his Russian ally President Vladimir Putin have rejected the accusations and criticised Poland for not taking the migrants in.
Polish media say at least 11 migrants have died since the crisis began in August.
Hope for de-escalating the crisis mounted this week, with German Chancellor Angela Merkel speaking with Lukashenko twice by phone—his first call with a Western leader since disputed presidential elections last year.
On Thursday, a day after the pair’s second call, the first repatriation flight for migrants landed in Iraq.
Lukashenko’s spokeswoman Natalya Eismont said on Thursday that there were about 7,000 migrants in the country in total.
She said Belarus will take responsibility for sending 5,000 of the migrants home if they want to go.
She alleged German chancellor Angela Merkel would negotiate with the EU on creating the humanitarian corridor to Germany, which Berlin has denied.