The deity is at least 5000 years old and was carved from Śaligrām-shīla by Lord Viṣvakarma himself on the order of Kṛṣṇa when Queen Rukmini (who was none other than Mahālakśmi) desired to worship Him in a childhood form when the latter was angry with her Husband for not allowing her into the rasā līlā.
He later came to Uḍupī and was installed by Śrilā Madhwācārya (the proponent of the Madhwā-sampradāyā) about 800 years ago in the present Udupi Kṛṣṇa Matt and is still being worshipped according to the standards set by him. A few additions were made 400 years later by Śripād Vādirājā Teerthā.
Uḍupī is called as "Dakṣina Dwārkā" (translates to "Dwārkā of south India) and it is said that one reaps the same spiritual benefits by visiting Udupi as they would by visiting Dwārkā.
Jai darling Udupi Kṛṣṇa!
Jai Śrilā Madhwācārya!
All glories to Śrilā Prabhupād! <3