Introduction Adolescents and youths who need exceptional healthcare are the shapers and leaders of our global future. However, many of them are died prematurely, while others suffer from diseases partly because of the poor quality of health services. Thus, this study aimed to assess the quality of Adolescent and Youth-friendly Health Services (AYFHS) and associated factors in the public health facilities of Dehana district, Northeast Ethiopia. Methods A facility-based quantitative cross-sectional study supported with a qualitative component was conducted from February 24 to March 30, 2020. The quality of AYFHS was measured using the Donbidean framework (structure, process and output component). Accordingly, a total of 431 adolescents and youths, five health facilities, twenty-five client-provider interaction observations, and nine key informant interviews were conducted. Binary logistic regression analysis was done, and variables with a p-value of < 0.05 and Adjusted Odds Ratio (AOR) with its 95% Confidence Interval (CI) were used to measure the association. The qualitative data were audio-recorded and transcribed verbatim. Then, Open Code 4.03 software was used to manage and analyze the data. Results The quality of adolescent and youth-friendly health services was 58.8, 46.4, and 47.2% for structural, process, and output quality dimensions, respectively. The predictor variables for output quality were, being a student (AOR: 2.07, 95%CI: 1.07–3.40), farmers (AOR: 2.59, 95%CI: 1.25–5.39), own income sources (AOR: 1.99, 95%CI: 1.03–3.85), exempted services (AOR: 2.30, 95%CI: 1.43–3.71) and long waiting time (AOR: 3.8495%CI: 1.80–8.23). Conclusions The overall quality of adolescent and youth-friendly health services was still lower than the WHO good quality standards. The structural quality dimension was affected by the unavailability of adequate and trained health service providers, poor engagement of adolescents and youths in the facility governance structure, unavailability of guidelines, protocols and procedures. In contrast, the process quality dimension was also compromised due to the provider’s poor compliance with the national AYFHS guidelines. Therefore, health facilities need to engage adolescents and youths in the health facility governance structure, and providers should comply with the national guideline.