(1) Background: One-day surgery has been widely adopted for many elective laparoscopic procedures in pediatric patients. Recently, the same protocol has been investigated for some emergency procedures, such as laparoscopic appendectomy. This study aimed to evaluate the safety and effectiveness of discharge from hospital within 24 h in pediatric patients who received laparoscopic appendectomy for uncomplicated acute appendicitis. (2) Methods: From 1 March 2021 to 1 May 2022, a total of 180 pediatric patients who were discharged from hospital within 24 h after laparoscopic appendectomy for uncomplicated appendicitis were included in this prospective single-center study. The primary outcome of this study was the safety of discharge from hospital within 24 h after laparoscopic appendectomy for uncomplicated appendicitis, as well as the parental satisfaction with this protocol. Secondary outcomes included the rate of readmission or unplanned return to the operating room, the complication rate and a cost-effectiveness analysis. For each patient, demographic data, preoperative evaluation (physical examination, laboratory data, imaging), duration of surgery, intraoperative and postoperative complications, length of hospital stay and pain levels, as well as parental satisfaction with this protocol, were recorded. (3) Results: The median age was 11 years (interquartile range (IQR) 10, 14). The majority of the patients (63.8%) were males. The median length of hospital stay after surgery was 15 h (IQR 12, 19). The highest level of satisfaction, at discharge, was recorded in most of the respondents (n = 155, 86.1%), while the remaining 25 (13.9%) expressed moderate levels of satisfaction. The median pain levels according to a visual analogue scale for all postoperative days were low (range 0–4). In four patients (2.2%), unplanned readmission before the seventh postoperative day because of postoperative intraabdominal abscess was recorded. All patients with abscess formation were treated conservatively. The majority of the parents (n = 175; 97.2%) expressed the highest level of satisfaction during the outpatient follow-up examination on the seventh postoperative day. (4) Conclusions: Same-day discharge after laparoscopic appendectomy for simple appendicitis in pediatric patients was safe and feasible. Parental satisfaction with this protocol was very high. With the right protocol and parent education, pediatric patients who underwent laparoscopic appendectomy because of non-complicated acute appendicitis may be successfully treated in this way.