diff --git a/CHANGELOG.md b/CHANGELOG.md
index af5011de4..6b1f76163 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -32,6 +32,10 @@ This project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.htm
 
 - The `ErrInvalidHexID`, `ErrInvalidTraceIDLength`, `ErrInvalidSpanIDLength`, `ErrInvalidSpanIDLength`, or `ErrNilSpanID` from the `go.opentelemetry.io/otel` package are unexported now. (#1243)
 
+### Fixed
+
+- The `go.opentelemetry.io/otel/api/global` packages global TextMapPropagator now delegates functionality to a globally set delegate for all previously returned propagators. (#1258)
+
 ## [0.13.0] - 2020-10-08
 
 ### Added
diff --git a/api/global/internal/propagator.go b/api/global/internal/propagator.go
new file mode 100644
index 000000000..706e024a6
--- /dev/null
+++ b/api/global/internal/propagator.go
@@ -0,0 +1,86 @@
+// Copyright The OpenTelemetry Authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package internal
+
+import (
+	"context"
+	"sync"
+
+	"go.opentelemetry.io/otel"
+)
+
+// textMapPropagator is a default TextMapPropagator that delegates calls to a
+// registered delegate if one is set, otherwise it defaults to delegating the
+// calls to a the default no-op otel.TextMapPropagator.
+type textMapPropagator struct {
+	mtx      sync.Mutex
+	once     sync.Once
+	delegate otel.TextMapPropagator
+	noop     otel.TextMapPropagator
+}
+
+// Compile-time guarantee that textMapPropagator implements the
+// otel.TextMapPropagator interface.
+var _ otel.TextMapPropagator = (*textMapPropagator)(nil)
+
+func newTextMapPropagator() *textMapPropagator {
+	return &textMapPropagator{
+		noop: otel.NewCompositeTextMapPropagator(),
+	}
+}
+
+// SetDelegate sets a delegate otel.TextMapPropagator that all calls are
+// forwarded to. Delegation can only be performed once, all subsequent calls
+// perform no delegation.
+func (p *textMapPropagator) SetDelegate(delegate otel.TextMapPropagator) {
+	if delegate == nil {
+		return
+	}
+
+	p.mtx.Lock()
+	p.once.Do(func() { p.delegate = delegate })
+	p.mtx.Unlock()
+}
+
+// HasDelegate returns if a delegate is set for p.
+func (p *textMapPropagator) HasDelegate() bool {
+	p.mtx.Lock()
+	defer p.mtx.Unlock()
+	return p.delegate != nil
+}
+
+// Inject set cross-cutting concerns from the Context into the carrier.
+func (p *textMapPropagator) Inject(ctx context.Context, carrier otel.TextMapCarrier) {
+	if p.HasDelegate() {
+		p.delegate.Inject(ctx, carrier)
+	}
+	p.noop.Inject(ctx, carrier)
+}
+
+// Extract reads cross-cutting concerns from the carrier into a Context.
+func (p *textMapPropagator) Extract(ctx context.Context, carrier otel.TextMapCarrier) context.Context {
+	if p.HasDelegate() {
+		return p.delegate.Extract(ctx, carrier)
+	}
+	return p.noop.Extract(ctx, carrier)
+}
+
+// Fields returns the keys who's values are set with Inject.
+func (p *textMapPropagator) Fields() []string {
+	if p.HasDelegate() {
+		return p.delegate.Fields()
+	}
+	return p.noop.Fields()
+}
diff --git a/api/global/internal/state.go b/api/global/internal/state.go
index e2ded6eb1..9542e60bf 100644
--- a/api/global/internal/state.go
+++ b/api/global/internal/state.go
@@ -41,8 +41,9 @@ var (
 	globalMeter       = defaultMeterValue()
 	globalPropagators = defaultPropagatorsValue()
 
-	delegateMeterOnce sync.Once
-	delegateTraceOnce sync.Once
+	delegateMeterOnce             sync.Once
+	delegateTraceOnce             sync.Once
+	delegateTextMapPropagatorOnce sync.Once
 )
 
 // TracerProvider is the internal implementation for global.TracerProvider.
@@ -96,6 +97,19 @@ func TextMapPropagator() otel.TextMapPropagator {
 
 // SetTextMapPropagator is the internal implementation for global.SetTextMapPropagator.
 func SetTextMapPropagator(p otel.TextMapPropagator) {
+	// For the textMapPropagator already returned by TextMapPropagator
+	// delegate to p.
+	delegateTextMapPropagatorOnce.Do(func() {
+		if current := TextMapPropagator(); current == p {
+			// Setting the provider to the prior default is nonsense, panic.
+			// Panic is acceptable because we are likely still early in the
+			// process lifetime.
+			panic("invalid TextMapPropagator, the global instance cannot be reinstalled")
+		} else if def, ok := current.(*textMapPropagator); ok {
+			def.SetDelegate(p)
+		}
+	})
+	// Return p when subsequent calls to TextMapPropagator are made.
 	globalPropagators.Store(propagatorsHolder{tm: p})
 }
 
@@ -113,16 +127,10 @@ func defaultMeterValue() *atomic.Value {
 
 func defaultPropagatorsValue() *atomic.Value {
 	v := &atomic.Value{}
-	v.Store(propagatorsHolder{tm: getDefaultTextMapPropagator()})
+	v.Store(propagatorsHolder{tm: newTextMapPropagator()})
 	return v
 }
 
-// getDefaultTextMapPropagator returns the default TextMapPropagator,
-// configured with W3C trace and baggage propagation.
-func getDefaultTextMapPropagator() otel.TextMapPropagator {
-	return otel.NewCompositeTextMapPropagator()
-}
-
 // ResetForTest restores the initial global state, for testing purposes.
 func ResetForTest() {
 	globalTracer = defaultTracerValue()