Kelp is a traditional healthy food due to its high nutritional content; however, its relatively high contents of iodine and arsenic have raised concerns about its edible safety. This study explored the effects of different cooking treatments on the contents of iodine and arsenic in kelp, evaluated the bioaccessibility and bioavailability of iodine and arsenic in kelp using in vitro digestion, and compared the differences in the transport characteristics of iodine in kelp and KIO using a Caco-2 monolayer cell transport model. The results show that the content of target elements that reached systemic circulation could be reduced by cooking and gastrointestinal digestion. The highest reductions in iodine and arsenic were 94.4% and 74.7%, respectively, which were achieved by boiling for 10 min. The bioaccessibility and bioavailability of iodine and arsenic were significantly improved by a cooking treatment. However, the contents of iodine and arsenic decreased significantly, with the bioaccessibility of iodine reducing from 3188.2 μg/L to 317.0 μg/L and that of arsenic reducing from 32.5 μg/L to 18.1 μg/L in the gastric phase after boiling. The findings also show that the efficiency of iodine transport in kelp and KIO was positively correlated with the transport time and negatively correlated with the concentration of iodine. With the increase in the iodine concentration, the rate of iodine transport in kelp decreased from 63.93% to 3.14%, but that of KIO was stable at around 35%, which indicates that the absorption efficiency of iodine from kelp was limited, even when too much kelp was ingested. In conclusion, the edible safety of kelp is significantly improved after cooking. The risk of excessive iodine and arsenic intake caused by consuming kelp is extremely low, and as an effective iodine supplement source, kelp has higher edible safety compared with KIO. This study clarifies the safety of algae based on iodine and arsenic contents and also provides a basis for the formulation of food safety standards.