The three Sahsranama stotrams dedicated to Lord Vishnu are found in Padma Purana,Skanda Purana and the Mahabharata.They are together called the "Trividha Vishnu Sahasranamams".Similarly,for Shiva we have "Chaturvidha Sahsranamams" but from Agama Texts we have many more.
Anyways,the verse in question appears within the Dhyana Sloka of the Vishnu Sahasranama that is from the Anushasanika Parva of Mahabharata.
Also, as you can see from the passage given below, that Vyasa is mentioned as the Rishi of the stotram so Vyasa only is the author of those verses.
Asya Shri Vishnordivya Sahasra naama Stotra Maha Mantrasya Shri Veda
Vyaaso Bhagavan Rishih Anushtup Chhandah Shri Maha Vishnuh Paramatmaa
Shrimannarayano Devata Amritaamshad –bhavo Bhanuriti beejam, Devaki
nandanassrashteti Shaktih,Udbhavah Kshobhano Deva iti paramo Mantrah
Shankha bhrinnandakeecha Chakriti keelakam, Sharangadhanvaa Gadaa
dhara ithystram Rathaanga paani rakshobhya iti netram, Trisaamaa
saamagassaameti kavacham, Aanandam Parabrahmeti yonih,
Rithussudarshanah Kaala iti digbandhah Vishwarupa itidhyanam Shri Maha
Vishnu preetyarthey kainkaryarupey Shri Vishnu Sahasra naama japey
viniyogah......
Dhyaanam: Ksheerodanvatpradeshe Shuchimani Vilasatsaikatey
Mouktikaanaam, Maalaaklaptaa –sanasthah Sphatika Mani nibhair
mouktikair manditaangaha/ Shubhrabhrairadabhrairupari virachitairmukta
peeyusha varshaih, Anandeenah puneeyaadari naleenagadaa shankha
paanirmukundah/ Bhu paadasya naabhirviyadadasrura nilaschandra
Suryoucha Netrey, Karnaavaashaashiro Dyormukhamkapi dakanoyasya
vaasyamdbhih/ Antastham yasya Vishwam Sura nara khaga Gobhogi
Gandharvadaityaschitramram Ramyate tam Tribhuvana vapusham Vishnu
meesham Namaami/ Shantaakaaram Bhujagashayanam Padmanaabham
Suresham, Vishwaakaaram Gagana sadrusham Meghavarnam Shubhangam/
Lakshmi kaantam Kamala nayanam Yogi hriddhyaana gamyam, Vandey Vishnum
Bhavabhayaharam Sarva Lokaika naatham/ Meghashyaamam Peetakousheya
vaasam Shri Vatsaangkam Koustubhodbhaasitangam,Punyopetam
Pundarikayataaksham Vishnum vandey Sarva Lokaika naatham/ Sashankha
chakram Sakireeta kundalam Sapeeta Vastram Saraseeruhekshanam, Sahaara
Vakshahsthala Koustubham Namaami Vishnum Shirasaa Chaturbhujam/ Harih
Om/
Meaning
May Bhagavan Mukunda purify us as he is seated on the Ocean of Milk in
the surroundings of sand that reflects the illumination of precious
gems while wearing garlands of pearls transparent like crystals and
adorned with Gada-Shankha-Chakra-Padma besides smiles of blissful
trance showering rains of nectar from pure clouds over head on the
blue skies; I salute Vishnu with admiration and deep veneration as He
his physique representing the Three Worlds apppears as though Earth is
His Sacred Feet, Sky His Navel, Air as His breathing, Sun and Moon as
His eyes, Dishas or Directions as His ears, Heaven as His head, Fire
as His Countenance and Oceans as His stomach. I salute Vishnu who
contains the Universe in totality with Devas, humanity, birds, cattle,
snakes, Gandharvas, Demons and so on all of whom act and play in
their own ways and means. I salute to and prostrate before Vishnu who
is the Paramount Power in all the Lokas as He is the embodiment of
Peace and Tranquility resting comfortably on Sesha Naaga as Padmanabha
or with a Lotus sprouted from his naabhi, Suresha or the Over Lord of
Sura Ganas, Vishwaakaaram or the Divine Profile of Vishwa or the
Universe, Gagana Sadrusham or like the most undefinable Skies, Neela
Varnam or of Blue complexion and Shubhangam or of the most auspicious
Physical Frame; Lakshmi Kantam or the family partner of Devi Lakshmi;
Kamala nayanam or of the enticing eyes of Lotus; Yogi hriddhyaana
gamyam or the Ultimate Goal of the heart-felt meditation of Yogis;
Bhavabhayaharam or the Single Saviour of the Dread and Distress of
Life’s Travails and the Unique Chief of all the Lokas; Bhagavan is
also renowned for His Physique of Cloud-like Blue Complexion, His
abode as the Ocean of Milk or dressed in yellow robes, Shri Vatsa mole
on his Chest, the bright Koustubha Mani on his body, Punyopetam or
surrounded by devotees and Dharmaatmas and of Lotus Eyes. Bhagavan is
famed as the ever-adorned with Shankha-Chakra-Kireeta-Kundala-Yellow
robes, Lotus like vision, Sacred and glitttering neck laces on chest
and the outstanding Koustubha all decorated on his Four Mighty Hands!
Indeed to that unparalleled Bhagavan Vishnu, my sincere salutations
and Prayers
Here is another link for the Vishnu Sahsranama Stotram from Mahabharata:
You can read the Dhyanam part from page 3 onwards and on page 5 we get the verses in your questions:

I'm unable to copy sanskrit verses from that document hence given the image as a reference.