The Bride Who Chose
The eighth book of the Bhagavata Purana tells how Lakshmi came to be the Lord's bride. It was not arranged for her. She chose.

Out of the ocean
When the gods and the asuras churned the ocean of milk, treasures rose from it one after another. Then Lakshmi appeared, and the Bhagavata says she was brighter than lightning on a marble mountain.
Everyone wanted her. They honoured her with gifts. Indra brought her a seat. The sacred rivers brought water in golden pots, and the earth gave herbs for her installation. Sages chanted, Gandharvas sang, and elephants bathed her with Ganges water. The ocean gave her yellow silk, Varuna a garland, and Vishvakarma, Sarasvati and Brahma gave her ornaments, a necklace and a lotus.
Then she stood with a garland of lotuses in her hand, shy and smiling, and went looking for a husband.
The search
She walked among them all: the Gandharvas, the Yakshas, the asuras, the Siddhas, the gods. And in every one she found a fault.
One was an ascetic, but had not conquered anger. One was learned, but had not conquered desire. One was great, but still depended on something else. One was religious, but not kind to all living beings. One was powerful, but could not stop time. Some had long lives but were not auspicious; some were auspicious but had short lives.
None was without a fault, and so she could take shelter in none of them.
The choice
At last she chose Mukunda, the Lord. The Bhagavata gives her reason: he was independent, and not in want of her. He had every good quality.
She placed her garland of fresh lotuses on his shoulders and stood at his side, smiling in shyness, hoping for a place on his chest. The Lord gave it to her. His chest became her home, forever.
The wedding retold
Every temple kalyanam retells this choice. The festival images of the Lord and his consort are brought face to face, the bride is given, garlands are exchanged, and the marriage is made again before the devotees.
At Yadagirigutta the groom is Narasimha. In the Bhagavata, after Hiranyakashipu's death, the gods asked Lakshmi to approach the Lord, but she had never seen such a form and was too afraid; it was Prahlada who went to him. At Yadagirigutta, Lakshmi is at his side, and the Lord is worshipped as Lakshmi Narasimha. The Narasimha avatar is told in The Narasimha Avatar: A Boon, a Pillar and a Doorway.
Tradition and record
The story of Lakshmi's choice is record: it stands in the Bhagavata Purana, book eight, chapter eight, and anyone can read it there. The English renderings in this article are paraphrases. The Bhagavata does not describe temple kalyanams; that couples take part in them seeking a happy married life is a living tradition, reported at Tirumala's celestial weddings, and not a statement of the text.