It is known that circulating DNA (cirDNA) is protected from nuclease activity by proteins that form macromolecular complexes with DNA. In addition, it was previously shown that cirDNA can bind to the outer surface of exosomes. NTA analysis and real-time PCR show that exosomes from healthy females (HF) or breast cancer patients (BCP) plasma contain less than 1.4 × 10−8 pg of DNA. Thus, only a minor part of cirDNA is attached to the outer side of the exosome as part of the vesicle crown: the share of exosomal DNA does not exceed 0.025% HF plasma DNA and 0.004% BCP plasma DNA. Treatment of plasma exosomes with DNase I with subsequent dot immunoassay reveals that H2a, H2b, and H3 histones are not part of the exosomal membrane, but are part of the cirDNA–protein macromolecular complex associated with the surface of the exosome either through interaction with DNA-binding proteins or with histone-binding proteins. Using bioinformatics approaches after identification by MALDI-TOF mass spectrometry, 16 exosomal DNA-binding proteins were identified. It was shown that four proteins—AIFM1, IGHM, CHD5, and KCNIP3—are candidates for DNA binding on the outer membrane of exosomes; the crown of exosomes may include five DNA-binding proteins: H2a, H2b, H3, IGHM, and ALB. Of note, AIFM1, IGHM, and CHD5 proteins are found only in HF plasma exosomes; KCNIP3 protein is identified only in BCP plasma exosomes; and H2a, H2b, H3, and ALB are revealed in all samples of plasma exosomes. Two histone-binding proteins, CHD5 and KDM6B, have been found in exosomes from HF plasma. The data obtained indicate that cirDNA preferentially binds to the outer membrane of exosomes by association with DNA-binding proteins.