She said her decision was not aimed at gaining any position in the party.
"I have joined the BJP neither to fight elections nor am I aiming for any position, but to work hard for assignments I will be given," Singh told reporters.
She praised Modi's policies and the changes he has made over the past three years.
"I wrote to Modi three years ago urging him to take up the triple talaq issue for protection of women. The way he has responded to it has satisfied me," she said.
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The disciplinary committee of Congress' Delhi unit removed Singh for indulging in "anti-party activities".
The development came on the eve of civic polls in the national capital.
Union Youth Affairs and Sports Minister Vijay Goel who was also present on the occasion said Singh's entry has strengthened the BJP.
"Congress leadership at both the national level and in Delhi is neither listening to its party members nor is is being able to satisfy its leaders," Goel said.