Reciting the Dattatreya Shlokas is one of the easiest ways to worship Lord Dattatreya, the combined incarnation of deities Brahma, Vishnu and Shiva (the holy trinity).
These Shlokas are powerful hymns for meditating on his divine form and connecting with his energy.
They praise Lord Dattatreya, his compassionate nature, appearance, divine attributes, and symbolism to a greater extent. Further, these Dattatreya Shlokas mention his incarnation as a great Guru, Avadutha and his association with Yoga and its related aspects.
Many devotees also combine these shlokas with the Datta Gayatri Mantra and other Dattatreya Mantras to invoke divine blessings, fulfil their wishes, and deepen their meditation.

Dattatreya Shlokas for Daily Worship
दत्तात्रेयं शिवं शान्तमिन्द्रनील-निभं विभुम्
आत्ममायारतं देवमवधूतं दिगम्बरम् ॥
भस्मोद्धूलित सर्वाङ्गं जटाजूटधरं विभुम्
चतुर्बाहुमुदारङ्गं प्रफुल्ल कमलेक्षणम् ॥
ज्ञानयोगनिधिं विश्वगुरुं योगिजनप्रियम्
भक्तानुकम्पिनं देवं दत्तात्रेयमहं भजे ॥
Dattātreyaṃ Śivaṃ Śāntaṃ Indranīla-Nibhaṃ Vibhum
Ātmamāyārataṃ Devamavadhūtaṃ Digambaram॥
Bhasmoddhūlita Sarvāṅgaṃ Jaṭājūṭadharaṃ Vibhum
Caturbāhum Udārāṅgaṃ Praphulla Kamalekṣaṇam॥
Jñānayoganidhiṃ Viśvaguruṃ Yogijanapriyam
Bhaktānukampinaṃ Devaṃ Dattātreyamaham Bhaje॥
Meaning: I worship Lord Dattatreya, who is auspicious and peaceful, whose complexion resembles the colour of a blue sapphire gemstone, O the all-pervading.
The one who delights in his own self, the God appearing in the form of an Avadhuta, the one clothed by the directions.
The all-pervading Lord, whose entire body is smeared with holy ash and is present with hair locks which are arranged beautifully.
Having four hands and a noble body, with eyes appearing like fully blossomed lotuses.
The Lord who is the treasure house of knowledge and Yoga, Guru of the Universe and dear to the Yogis.
The very compassionate towards his devotees, O that Lord Dattatreya, I worship you.
दत्तात्रेयं भस्म सुगन्धलेपनं चक्रं त्रिशूलं डमरुं गदां च ।
पद्मासनस्थं शशिसूर्यनेत्रं ध्यायेत् सदा दत्तमभीष्टसिद्धिदम् ॥
Dattātreyaṃ Bhasma Sugandhalepanaṃ Cakraṃ Triśūlaṃ Ḍamaruṃ Gadāṃ Ca।
Padmāsanasthaṃ Śaśisūrya-netraṃ Dhyāyet Sadā Dattam Abhīṣṭasiddhidam ॥
Meaning: O Lord Dattatreya, whose body is smeared with sacred ash (Bhasma) and with fragrant pastes (like Sandalwood, Kasturi, and Agar). Who holds a discus, trident, drum, and mace in his hands. The one seated in a yoga posture of Padmasana (lotus pose), whose eyes are none other than the moon and sun. I always worship Lord Datta, who fulfils the desired wishes of the devotees.
योगारूढं योगपट्टोपवीतं
हस्तद्वन्द्वं जानुयुग्मे प्रसार्य ।
अंसाग्रस्थं दिव्यभूषितजटाकं
दत्तात्रेयं भावये वीक्ष्यमाणम् ॥
Yogārūḍha Yogapaṭopavītaṃ
Hastadvandvaṃ Januyugme Prasārya।
Aṃsāgrasthaṃ Divyabhūṣita jatākaṃ
Dattātreyaṃ Bhāvaye Vīkṣyamāṇam॥
Meaning: Seated in a Yogic posture, wearing the Yoga patta (a cloth band or strap used to hold legs and lower back in the yogic position) and Upavita (sacred thread worn to perform Hindu rituals). Having his two hands stretched forth upon his two knees (like in the yoga posture Yogapattasana).
Whose resting edges of the shoulders are adorned with golden ornaments and the one having matted hair. I visualise and worship that form of Lord Dattatreya.
Dattatreya Dhyana Shloka
सदानन्दात्मकं शुद्धं सात्त्विकं तारकं परम् ।
विश्वरूपं जगद्योनिं दत्तात्रेयं भजाम्यहम् ॥
Sadānandātmakaṃ Śuddhaṃ Sāttvikaṃ Tārakaṃ Param ।
Viśvarūpaṃ Jagadyoniṃ Dattātreyaṃ Bhajāmyaham ॥
Meaning: (I worship Lord Dattatreya) The one whose very nature is eternal bliss, who is pure and filled with serene goodness. The great liberator and the supreme being. Whose form is the entire cosmos and the one who is the source of the universe (entire creation). I worship that, Lord Dattatreya.