River channel geometry is often controlled by upstream boundary conditions, including fluvial discharge and sediment properties. At the coast, downstream boundary conditions (e.g., tides, waves, water depth) also strongly influence channel formation and evolution. We conducted a set of experiments to determine the effects of basin water depth (i.e., a downstream boundary condition) on the evolution and geometry of fluviodeltaic channels and lobes. Internal dynamics (autogenic processes) in the fluviodeltaic system drive channel avulsion through cycles of sediment storage and release. Experimental results indicate an increase in the timescale of autogenic storage and release with increasing basin water depth. Deeper basin water requires a larger volume to be filled within the delta front, thus more time to complete one autogenic storage and release cycle for a given sediment discharge. While a relationship between delta-front volume and autogenic storage and release timescales is expected, we show that autogenically generated morphological changes in the delta topset and distributary channels also exert control on timescales of storage and release. Deltas building into deeper basins develop steeper topsets, and deeper distributary channels that cause high-magnitude topset slope fluctuations, which contribute to the long autogenic timescales. Deposits in shallow basins exhibit both shallower topset slopes and shallower channels. Channel bed slopes are similar (∼ 0.06) across all experiments, but lateral channel migration rates varied with basin depth. Deltas building into shallow basins had rapid lateral channel migration, such that channels quickly reworked the delta topset. For deep basins, channel migration rates were much slower, so the topset was reworked less often, allowing the topset to build to steeper slopes before being reworked. These experiments indicate an intimate relationship between lateral channel migration and topset aggradation. In addition, the deeper and more stable channels in deeper basins generally developed a wider range of channel widths, some of which produced elongate lobes. We conclude that the downstream boundary has a strong control on fluviodeltaic morphology, which can result in a striking difference in the autogenic timescale.