Niger's armed forces have so far picked up 1,397 people, many of them women and children, according to a statement from the army's southeastern region, seen by AFP.
They have been handed over to the Nigerian military authorities, it said.
"Around 30 terrorists" who refused to surrender were killed, it added.
The exodus into southeastern Niger started in March, when the Islamic State West Africa Province (ISWAP) pursued Boko Haram in its forest hideout of Sambisa, northeastern Niger.
The Boko Haram followers were trying to reach the marshlands of the vast Lake Chad region, whose islands have long been a bolt hole for jihadists.
The movement was first spotted on March 7, as people walked along the Kamadougou Yoge River marking the border between the two countries.
Six days later, Nigerien troops in a regional anti-jihadist task force launched an operation that killed 20 jihadists and captured 83 others, according to the army.
The southeastern region of Diffa, which has born the brunt of jihadist attacks over the years, has been relatively calm since the start of 2023, a security source told AFP.
However, land mines sown by rebels continue to claim lives. Last month, seven soldiers died and nearly a dozen were wounded in blasts.
Boko Haram launched a bloody campaign in northeastern Nigeria in 2009 that has left over 40,000 dead and displaced around two million from their homes, according to UN figures.
It became globally notorious in 2014 for abducting 276 schoolgirls in the town of Chibok, 96 of whom remain missing.
But the group split in 2016, giving birth to ISWAP, which now dominates in a fratricidal conflict.