Heterogeneous　networks　(HetNets)　with　end-to-end　(E2E)　network　slicing　are　regarded　as　effective　approaches　to　meet　diverse　service　requirements　from　vertical　industries.　Due　to　the　dense　deployment　of　base　stations　(BSs)　and　the　complicated　associations　between　BSs　and　E2E　network　slices　(NSs)　in　the　scenario,　the　handoff　problem　faces　challenges　of　the　huge　system　state　space　and　handoff　action　space　and　the　considerable　communication　overhead.　In　this　paper,　we　take　these　issues　into　account　and　consider　a　distributed　E2E　NS　handoff　decision　framework　in　the　HetNet.　A　decentralized　Markov　decision　process　(DEC-MDP)-based　model　is　formulated　for　the　distributed　E2E　NS　handoff　problem,　and　the　jointly　observable　and　random　characteristics　of　the　DEC-MDP　are　analyzed.　To　obtain　a　theoretical　performance　reference,　the　original　distributed　E2E　NS　handoff　problem　is　simplified,　and　a　Nash　equilibrium-based　performance　bound　is　given.　More　practically,　the　multi-agent　double　deep　Q-network-based　distributed　handoff　(MA-DDQN-DH)　algorithm　with　the　centralized　training　and　decentralized　executing　framework　is　proposed.　Simulation　results　show　that　the　Nash　equilibrium-based　performance　bound　is　reasonable,　and　the　proposed　MA-DDQN-DH　algorithm　performs　well　in　the　comparison.