Federated learning (FL) has garnered considerable interest for its capability to learn from decentralized data sources. Given the increasing application of FL in decision-making scenarios, addressing fairness issues across different sensitive groups (e.g., female, male) in FL is crucial. Current research often focuses on facilitating fairness at each client's data (local fairness) or within the entire dataset across all clients (global fairness). However, existing approaches that focus exclusively on either local or global fairness fail to address two key challenges: (\textbf{CH1}) Under statistical heterogeneity, global fairness does not imply local fairness, and vice versa. (\textbf{CH2}) Achieving fairness under model-agnostic setting. To tackle the aforementioned challenges, this paper proposes a novel post-processing framework for achieving both Local and Global Fairness in the FL context, namely LoGoFair. To address CH1, LoGoFair endeavors to seek the Bayes optimal classifier under local and global fairness constraints, which strikes the optimal accuracy-fairness balance in the probabilistic sense. To address CH2, LoGoFair employs a model-agnostic federated post-processing procedure that enables clients to collaboratively optimize global fairness while ensuring local fairness, thereby achieving the optimal fair classifier within FL. Experimental results on three real-world datasets further illustrate the effectiveness of the proposed LoGoFair framework.