diff --git a/kernel/src/main/scala/cats/kernel/instances/DoubleInstances.scala b/kernel/src/main/scala/cats/kernel/instances/DoubleInstances.scala
index 240a69b54e..77552070bb 100644
--- a/kernel/src/main/scala/cats/kernel/instances/DoubleInstances.scala
+++ b/kernel/src/main/scala/cats/kernel/instances/DoubleInstances.scala
@@ -36,9 +36,23 @@ class DoubleGroup extends CommutativeGroup[Double] {
 
 class DoubleOrder extends Order[Double] with Hash[Double] {
 
-  def hash(x: Double): Int = x.hashCode()
+  // Canonicalize +0.0 / -0.0 so Hash agrees with eqv (primitive ==).
+  // java.lang.Double.hashCode distinguishes the two zeros via bit patterns.
+  def hash(x: Double): Int =
+    java.lang.Double.hashCode(if (x == 0.0) 0.0 else x)
+
+  /**
+   * Compare using primitive relational operators so +0.0 and -0.0 are equal,
+   * matching [[eqv]] / IEEE floating equality. `java.lang.Double.compare`
+   * implements a total order that treats them as different, which made
+   * `Order[Option[Double]].eqv` disagree with `Order[Double].eqv` (#4807).
+   * NaN values fall through to `Double.compare` for a stable total order.
+   */
   def compare(x: Double, y: Double): Int =
-    java.lang.Double.compare(x, y)
+    if (x < y) -1
+    else if (x > y) 1
+    else if (x == y) 0
+    else java.lang.Double.compare(x, y)
 
   override def eqv(x: Double, y: Double): Boolean = x == y
   override def neqv(x: Double, y: Double): Boolean = x != y
diff --git a/kernel/src/main/scala/cats/kernel/instances/FloatInstances.scala b/kernel/src/main/scala/cats/kernel/instances/FloatInstances.scala
index 42b0838694..0b0d230117 100644
--- a/kernel/src/main/scala/cats/kernel/instances/FloatInstances.scala
+++ b/kernel/src/main/scala/cats/kernel/instances/FloatInstances.scala
@@ -47,10 +47,23 @@ class FloatGroup extends CommutativeGroup[Float] {
  */
 class FloatOrder extends Order[Float] with Hash[Float] {
 
-  def hash(x: Float): Int = x.hashCode()
+  // Canonicalize +0.0f / -0.0f so Hash agrees with eqv (primitive ==).
+  // java.lang.Float.hashCode distinguishes the two zeros via bit patterns.
+  def hash(x: Float): Int =
+    java.lang.Float.hashCode(if (x == 0.0f) 0.0f else x)
 
+  /**
+   * Compare using primitive relational operators so +0.0f and -0.0f are equal,
+   * matching [[eqv]] / IEEE floating equality. `java.lang.Float.compare`
+   * implements a total order that treats them as different, which made
+   * `Order[Option[Float]].eqv` disagree with `Order[Float].eqv` (#4807).
+   * NaN values fall through to `Float.compare` for a stable total order.
+   */
   def compare(x: Float, y: Float): Int =
-    java.lang.Float.compare(x, y)
+    if (x < y) -1
+    else if (x > y) 1
+    else if (x == y) 0
+    else java.lang.Float.compare(x, y)
 
   override def eqv(x: Float, y: Float): Boolean = x == y
   override def neqv(x: Float, y: Float): Boolean = x != y
diff --git a/tests/shared/src/test/scala/cats/tests/OrderSuite.scala b/tests/shared/src/test/scala/cats/tests/OrderSuite.scala
index 9901ade6eb..44f09a65da 100644
--- a/tests/shared/src/test/scala/cats/tests/OrderSuite.scala
+++ b/tests/shared/src/test/scala/cats/tests/OrderSuite.scala
@@ -76,6 +76,31 @@ class OrderSuite extends CatsSuite {
     assert(OrderOfCmpSub.gt(OrderSuite.CmpSub(2, "ignored"), OrderSuite.CmpSub(1, "ignored")))
     assert(OrderOfCmpSub.eqv(OrderSuite.CmpSub(1, "a"), OrderSuite.CmpSub(1, "b")))
   }
+
+  // #4807: +0.0 and -0.0 must agree across eqv, compare, and derived Option eqv
+  test("#4807 Double signed zeros are equal under Order and Option") {
+    val pos = 0.0
+    val neg = -0.0
+    assert(Order[Double].eqv(pos, neg))
+    assertEquals(Order[Double].compare(pos, neg), 0)
+    assert(cats.kernel.Hash[Double].hash(pos) === cats.kernel.Hash[Double].hash(neg))
+    assert(Order[Option[Double]].eqv(Some(pos), Some(neg)))
+    assertEquals(Order[Option[Double]].compare(Some(pos), Some(neg)), 0)
+    assert((Some(pos): Option[Double]) === (Some(neg): Option[Double]))
+    assert(pos === neg)
+  }
+
+  test("#4807 Float signed zeros are equal under Order and Option") {
+    val pos = 0.0f
+    val neg = -0.0f
+    assert(Order[Float].eqv(pos, neg))
+    assertEquals(Order[Float].compare(pos, neg), 0)
+    assert(cats.kernel.Hash[Float].hash(pos) === cats.kernel.Hash[Float].hash(neg))
+    assert(Order[Option[Float]].eqv(Some(pos), Some(neg)))
+    assertEquals(Order[Option[Float]].compare(Some(pos), Some(neg)), 0)
+    assert((Some(pos): Option[Float]) === (Some(neg): Option[Float]))
+    assert(pos === neg)
+  }
 }
 
 object OrderSuite {